C₃²×D₇×C₂₃ #15668484

order	2898
isoclinism	isoclinic class of D₇
automorphism	?
homology	Abelianization (H₁) = C₂×C₃²×C₂₃ · Schur multiplier (H₂) = C₃

Aliases

C₃²×D₇×C₂₃

	subgroup	G/H
center, hypercenter	C₃²×C₂₃	D₇
commutator, cosocle, hypocenter	C₇	C₂×C₃²×C₂₃
Frattini	C₁	G
Fitting, socle	C₃²×C₇×C₂₃	C₂
LCS	G ▷ C₇
UCS	C₁ ◁ C₃²×C₂₃

48 conjugacy classes of subgroups.

minimal degree	μ(G) = 36
transitive degree	μ_t(G) = 1449

A minimal faithful permutation representation — 2 generators on 36 points:

(1,2,3)(7,8,9,10,11,12,13)(14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36);(4,5,6)(8,13)(9,12)(10,11)

1035 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2898, 23);