C₂²×C₃²×3₋¹⁺² #11758142

order	972
nilpotency class	2
isoclinism	isoclinic class of H(3,𝔽₃)
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃⁴ · Schur multiplier (H₂) = C₂×C₃⁵

Aliases

C₂²×C₃²×3₋¹⁺²

	subgroup	G/H
center, socle	C₂²×C₃³	C₃²
commutator, Frattini, cosocle	C₃	C₂²×C₃⁴
prime radical	C₂²×C₃⁴	C₃
LCS	G ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₂²×C₃³ ◁ G

1440 conjugacy classes of subgroups.

minimal degree	μ(G) = 19
transitive degree	μ_t(G) = 324

A minimal faithful permutation representation — 4 generators on 19 points:

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(972, 867);