C₂²×C₃×D₄×3₋¹⁺² #72268907

order	2592
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃³ · Schur multiplier (H₂) = C₂⁶×C₃²

Aliases

C₂²×C₃×D₄×3₋¹⁺²

	subgroup	G/H
center, socle	C₂³×C₃²	C₂²×C₃²
commutator, Frattini, cosocle	C₂×C₃	C₂⁴×C₃³
prime radical	C₂²×C₃³×D₄	C₃
LCS	G ▷ C₂×C₃ ▷ C₁
UCS	C₁ ◁ C₂³×C₃² ◁ G

4484 conjugacy classes of subgroups.

minimal degree	μ(G) = 20
transitive degree	μ_t(G) = 432

A minimal faithful permutation representation — 4 generators on 20 points:

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

660 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)(13,15,18)(16,20,19), (3,4)(12,13,16,17,18,20,14,15,19), (5,6,7)(9,11), (8,9,10,11));