C₂×C₁₃×C₁₁⋊C₅ #13083643

order	1430
isoclinism	isoclinic class of C₁₁⋊C₅
automorphism	?
homology	Abelianization (H₁) = C₂×C₅×C₁₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₂×C₁₃×C₁₁⋊C₅
unambiguous semidirect product	(C₂×C₁₁)⋊(C₅×C₁₃)
unambiguous semidirect product	(C₂×C₁₁×C₁₃)⋊C₅

	subgroup	G/H
center, hypercenter	C₂×C₁₃	C₁₁⋊C₅
commutator, cosocle, hypocenter	C₁₁	C₂×C₅×C₁₃
Frattini	C₁	G
Fitting, socle	C₂×C₁₁×C₁₃	C₅
LCS	G ▷ C₁₁
UCS	C₁ ◁ C₂×C₁₃

16 conjugacy classes of subgroups.

minimal degree	μ(G) = 26
transitive degree	μ_t(G) = 286

A minimal faithful permutation representation — 2 generators on 26 points:

(1,2)(3,4,5,6,7,8,9,10,11,12,13,14,15)(17,18,20,23,22)(19,21,25,26,24);(16,17,19,22,18,20,24,26,21,23,25)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1430, 4);