C₂×D₄²×C₂²⋊C₄ #72324036

order	2048
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂⁶×C₄ · Schur multiplier (H₂) = C₂²²

Aliases

C₂×D₄²×C₂²⋊C₄

1092460 conjugacy classes of subgroups.

minimal degree	μ(G) = 18
transitive degree	μ_t(G) = 256

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

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

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

maximal subgroup of	C₂×D₄²×#120
maximal normal subgroup of	C₂×D₄²×#120

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

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