C₃²×C₁₁⋊C₅ #92464

order	495
isoclinism	isoclinic class of C₁₁⋊C₅
automorphism	?
homology	Abelianization (H₁) = C₃²×C₅ · Schur multiplier (H₂) = C₃

Aliases

direct product	C₃²×C₁₁⋊C₅
unambiguous semidirect product	C₁₁⋊(C₃²×C₅)
unambiguous semidirect product	(C₃×C₁₁)⋊(C₃×C₅)
unambiguous semidirect product	(C₃²×C₁₁)⋊C₅

Fitting, socle, Hall	C₃²×C₁₁ ⋊ C₅
derived, Sylow	C₁₁ ⋊ C₃²×C₅

	subgroup	G/H
center, hypercenter	C₃²	C₁₁⋊C₅
commutator, cosocle, hypocenter	C₁₁	C₃²×C₅
Frattini	C₁	G
Fitting, socle	C₃²×C₁₁	C₅
LCS	G ▷ C₁₁
UCS	C₁ ◁ C₃²

24 conjugacy classes of subgroups.

minimal degree	μ(G) = 17
transitive degree	μ_t(G) = 99

A minimal faithful permutation representation — 2 generators on 17 points:

(4,5,6)(8,9,11,14,13)(10,12,16,17,15);(1,2,3)(7,8,10,13,9,11,15,17,12,14,16)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(495, 3);