C₇×A₄×C₂₃ #14515390

order	1932
isoclinism	isoclinic class of A₄
automorphism	?
homology	Abelianization (H₁) = C₃×C₇×C₂₃ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₇×A₄×C₂₃
unambiguous semidirect product	C₂²⋊(C₃×C₇×C₂₃)
unambiguous semidirect product	(C₂²×C₂₃)⋊(C₃×C₇)

	subgroup	G/H
center, hypercenter	C₇×C₂₃	A₄
commutator, cosocle, hypocenter	C₂²	C₃×C₇×C₂₃
Frattini	C₁	G
Fitting, socle	C₂²×C₇×C₂₃	C₃
LCS	G ▷ C₂²
UCS	C₁ ◁ C₇×C₂₃

20 conjugacy classes of subgroups.

minimal degree	μ(G) = 34
transitive degree	μ_t(G) = 644

A minimal faithful permutation representation — 2 generators on 34 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);(8,9,10)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1932, 25);