C₂²×D₄×C₉⋊C₉ #72268934

order	2592
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃×C₉ · Schur multiplier (H₂) = C₂⁶×C₃

Aliases

C₂²×D₄×C₉⋊C₉

2006 conjugacy classes of subgroups.

minimal degree	μ(G) = 26
transitive degree	μ_t(G) = 1296

A minimal faithful permutation representation — 4 generators on 26 points:

(1,2)(9,10,12,11,13,15,14,16,17)(19,21,24)(22,26,25);(3,4)(18,19,22,23,24,26,20,21,25);(6,8);(5,6,7,8)

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

maximal subgroup of	C₂²×D₄×#6900
maximal normal subgroup of	C₂²×D₄×#6900

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

gap> G := Group((1,2)(9,10,12,11,13,15,14,16,17)(19,21,24)(22,26,25), (3,4)(18,19,22,23,24,26,20,21,25), (6,8), (5,6,7,8));