D₃×C₇×D₇×C₂₃ #27214189

order	13524
automorphism	?
homology	Abelianization (H₁) = C₂²×C₇×C₂₃ · Schur multiplier (H₂) = C₂

Aliases

direct product	D₃×C₇×D₇×C₂₃
unambiguous semidirect product	(D₃×C₇)⋊(C₂×C₇×C₂₃)
unambiguous semidirect product	(C₃×D₇)⋊(C₂×C₇×C₂₃)
unambiguous semidirect product	D₂₁⋊(C₂×C₇×C₂₃)

	subgroup	G/H
center, hypercenter	C₇×C₂₃	D₃×D₇
commutator, cosocle, hypocenter	C₃×C₇	C₂²×C₇×C₂₃
Frattini	C₁	G
Fitting, socle	C₃×C₇²×C₂₃	C₂²
LCS	G ▷ C₃×C₇
UCS	C₁ ◁ C₇×C₂₃

104 conjugacy classes of subgroups.

minimal degree	μ(G) = 40
transitive degree	μ_t(G) = 966

A minimal faithful permutation representation — 2 generators on 40 points:

(1,2,3,4,5,6,7)(9,10)(11,12)(13,14)(15,16,17)(18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40);(8,9,11,13,14,12,10)(16,17)

2415 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13524, 123);