C₂₉×C₁₁⋊C₅ #13097576

order	1595
isoclinism	isoclinic class of C₁₁⋊C₅
automorphism	?
homology	Abelianization (H₁) = C₅×C₂₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₂₉×C₁₁⋊C₅
unambiguous semidirect product	C₁₁⋊(C₅×C₂₉)
unambiguous semidirect product	(C₁₁×C₂₉)⋊C₅

Fitting, socle, Hall	C₁₁×C₂₉ ⋊ C₅
derived, Sylow	C₁₁ ⋊ C₅×C₂₉

	subgroup	G/H
center, hypercenter	C₂₉	C₁₁⋊C₅
commutator, cosocle, hypocenter	C₁₁	C₅×C₂₉
Frattini	C₁	G
Fitting, socle	C₁₁×C₂₉	C₅
LCS	G ▷ C₁₁
UCS	C₁ ◁ C₂₉

8 conjugacy classes of subgroups.

minimal degree	μ(G) = 40
transitive degree	μ_t(G) = 319

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1595, 1);