C₄×#6855 #11757340

order	972
nilpotency class	2
isoclinism	isoclinic class of H(3,𝔽₃)
automorphism	?
homology	Abelianization (H₁) = C₄×C₉² · Schur multiplier (H₂) = C₃³

Aliases

	subgroup	G/H
center	C₃³×C₄	C₃²
commutator	C₃	C₄×C₉²
Frattini, socle, prime radical, cosocle	C₂×C₃³	C₂×C₃²
LCS	G ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃³×C₄ ◁ G

207 conjugacy classes of subgroups.

minimal degree	μ(G) = 31
transitive degree	μ_t(G) = 972

A minimal faithful permutation representation — 2 generators on 31 points:

(1,2,3,4)(5,6,8)(7,10,12)(9,13,11)(14,15,17,16,18,20,19,21,22);(6,9,10)(8,12,13)(23,24,26,25,27,29,28,30,31)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(972, 65);