C₅×(C₃⋊D₃)⋊D₁₃ #14556830

order	2340
isoclinism	isoclinic class of (C₃⋊D₃)⋊D₁₃
automorphism	?
homology	Abelianization (H₁) = C₂²×C₅ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₅×(C₃⋊D₃)⋊D₁₃
unambiguous semidirect product	(C₃⋊D₃)⋊(C₅×D₁₃)
unambiguous semidirect product	D₃₉⋊(C₅×D₃)

	subgroup	G/H
center, hypercenter	C₅	(C₃⋊D₃)⋊D₁₃
commutator, cosocle, hypocenter	C₃²×C₁₃	C₂²×C₅
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₁₃	C₂²
LCS	G ▷ C₃²×C₁₃
UCS	C₁ ◁ C₅

88 conjugacy classes of subgroups.

minimal degree	μ(G) = 24
transitive degree	μ_t(G) = 390

A minimal faithful permutation representation — 2 generators on 24 points:

(1,2,3,4,5)(6,7)(10,11)(12,13,15,17,19,21,23,24,22,20,18,16,14);(7,8)(9,10,11)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2340, 134);