C₂³×D₄×C₄⋊C₄ #72289358

order	1024
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂⁶×C₄ · Schur multiplier (H₂) = C₂²¹

Aliases

C₂³×D₄×C₄⋊C₄

206261 conjugacy classes of subgroups.

minimal degree	μ(G) = 18
transitive degree	μ_t(G) = 512

A minimal faithful permutation representation — 7 generators on 18 points:

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

400 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((11,12,13,14), (3,4), (8,10)(11,12,13,14)(15,16,17,18), (11,12)(13,14), (7,8,9,10), (5,6), (1,2)(3,4)(5,6));