C₂²×D₄×#6900 #72268935

order	7776
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃³ · Schur multiplier (H₂) = C₂⁶×C₃

Aliases

C₂²×D₄×#6900

	subgroup	G/H
center, socle	C₂³×C₃²	C₂²×C₃³
commutator, Frattini, cosocle	C₂×C₃²	C₂⁴×C₃³
prime radical	C₂²×C₃³×D₄	C₃²
LCS	G ▷ C₂×C₃² ▷ C₁
UCS	C₁ ◁ C₂³×C₃² ◁ G

8260 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)(10,12,15)(13,17,16)(19,21,24)(22,26,25);(3,4)(9,10,13,14,15,17,11,12,16);(6,8)(18,19,22,23,24,26,20,21,25);(5,6,7,8)

1020 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)(10,12,15)(13,17,16)(19,21,24)(22,26,25), (3,4)(9,10,13,14,15,17,11,12,16), (6,8)(18,19,22,23,24,26,20,21,25), (5,6,7,8));