Order = 4080 = 24.3.5.17.
Mult = 1.
Out = 4.

Porting notes

Porting incomplete.

Standard generators

Standard generators of L2(16) are a, b where a has order 2, b has order 3 and ab has order 15.

Standard generators of L2(16):2 are c, d where c is in class 2B, d has order 4 and cd has order 15.

Standard generators of L2(16):4 are e, f where e is in class 2A, f is in class 4B/B', ef has order 8, eff has order 6 and efeffefff has order 4.

Black box algorithms

Checking generators (semi-presentations)

Group Semi-presentation File

Presentations

L2(16) a, b | a2 = b3 = (ab)15 = ((ab)5(ab−1)3)2 = 1 〉 Details
L2(16):2 c, d | c2 = d4 = [c, dcd]2 = cd(cdcd2)2(cd2cd)2cdcd−1 = 1 〉 Details
L2(16):4 e, f | e2 = f4 = (ef)8 = (ef2)6 = (ef)3(ef−1)3(ef)2(ef−1)2(ef)2ef2 = 1 〉 Details

Conjugacy classes

Conjugacy classes of L2(16)

Conjugacy class Centraliser order Power up Class rep(s)
1A 4 080 aa
2A 16 a
3A 15 (ab)5
5A 15 (abab)3
5B 15 (ab)3
15A 15 ab
15B 15 abababab
15C 15 abab
15D 15 abababababababab
17A 17 ababb
17B 17 ababbababbababbababb
17C 17 ababbababb
17D 17 ababbababbababbababbababbababbababbababb
17E 17 (ababbababb)3
17F 17 (ababbababbababbababbababbababbababbababb)3
17G 17 (ababbababbababbababb)3
17H 17 (ababb)3

Conjugacy classes of L2(16):2

Conjugacy class Centraliser order Power up Class rep(s)
1A 8 160 cdcdcddcdcdcddcdcdcddcdcdcdd
2A 32 cdcdcddcdcdcdd
3A 30 cdcddcdcdd
5A 30 cddcddcddcdd
5B 30 cddcdd
15A 15 cd
15C 15 cdcd
17A 17 (cdcdcdddcdcdcddd)3
17C 17 (cdcdcddd)3
17E 17 cdcdcdddcdcdcddd
17G 17 cdcdcddd
2B 120 (cdcdd)3
4A 8 cdcdcdd
6A 6 cdcdd
10A 10 cdd
10B 10 (cdd)3

Conjugacy classes of L2(16):4

Conjugacy class Centraliser order Power up Class rep(s)
1A 16 320 (ef)8
2A 64 (ef)4
3A 60 (efeff)4
5A 30 (efefeffeff)2
15A 15 efefeff
17A 17 (efefff)3
17E 17 efefff
2B 240 (efeff)6
4A 16 (ef)2
6A 12 (efeff)2
10A 10 efefeffeff
4B 24 (efeff)3
4B' 24 (efeff)9
8A 8 ef
8A' 8 (ef)3
12A 12 (efeff)7
12A' 12 efeff