C₅×A₄×C₂₃ #13063418

order	1380
isoclinism	isoclinic class of A₄
automorphism	?
homology	Abelianization (H₁) = C₃×C₅×C₂₃ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₅×A₄×C₂₃
unambiguous semidirect product	C₂²⋊(C₃×C₅×C₂₃)
unambiguous semidirect product	(C₂²×C₅)⋊(C₃×C₂₃)
unambiguous semidirect product	(C₂²×C₂₃)⋊(C₃×C₅)
unambiguous semidirect product	(C₂²×C₅×C₂₃)⋊C₃

	subgroup	G/H
center, hypercenter	C₅×C₂₃	A₄
commutator, cosocle, hypocenter	C₂²	C₃×C₅×C₂₃
Frattini	C₁	G
Fitting, socle	C₂²×C₅×C₂₃	C₃
LCS	G ▷ C₂²
UCS	C₁ ◁ C₅×C₂₃

20 conjugacy classes of subgroups.

minimal degree	μ(G) = 32
transitive degree	μ_t(G) = 460

A minimal faithful permutation representation — 2 generators on 32 points:

(1,2,3,4,5)(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);(6,7,8)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1380, 21);