C₂×D₃×C₈×D₈ #72226266

order	1536
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₈ · Schur multiplier (H₂) = C₂¹⁰

Aliases

C₂×D₃×C₈×D₈

Fitting	C₂×C₃×C₈×D₈ ⋊ C₂
Sylow	C₃ ⋊ C₂²×C₈×D₈

5492 conjugacy classes of subgroups.

minimal degree	μ(G) = 21
transitive degree	μ_t(G) = 384

A minimal faithful permutation representation — 5 generators on 21 points:

(1,2,3)(14,16,18,15,19,20,17,21);(6,7,8,10,9,11,12,13)(14,15,17,16,19,21,18,20);(4,5);(2,3);(15,20)(16,21)(17,18)

336 conjugacy classes. The character table is too large to display.

Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:

gap> G := Group((1,2,3)(14,16,18,15,19,20,17,21), (6,7,8,10,9,11,12,13)(14,15,17,16,19,21,18,20), (4,5), (2,3), (15,20)(16,21)(17,18));