C₃²×D₅×C₁₃ #11924064

order	1170
isoclinism	isoclinic class of D₅
automorphism	?
homology	Abelianization (H₁) = C₂×C₃²×C₁₃ · Schur multiplier (H₂) = C₃

Aliases

direct product	C₃²×D₅×C₁₃
unambiguous semidirect product	C₅⋊(C₂×C₃²×C₁₃)

	subgroup	G/H
center, hypercenter	C₃²×C₁₃	D₅
commutator, cosocle, hypocenter	C₅	C₂×C₃²×C₁₃
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₁₃	C₂
LCS	G ▷ C₅
UCS	C₁ ◁ C₃²×C₁₃

48 conjugacy classes of subgroups.

minimal degree	μ(G) = 24
transitive degree	μ_t(G) = 585

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

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1170, 22);