C₄×C₉² #66334

order	324
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 7776
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₉

Aliases

C₄×C₉²

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

69 conjugacy classes of subgroups.

minimal degree	μ(G) = 22
transitive degree	μ_t(G) = 324

A minimal faithful permutation representation — 2 generators on 22 points:

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(324, 26);