C₅×C₁₃×D₉ #11924050

order	1170
isoclinism	isoclinic class of D₉
automorphism	?
homology	Abelianization (H₁) = C₂×C₅×C₁₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₅×C₁₃×D₉
unambiguous semidirect product	C₉⋊(C₂×C₅×C₁₃)

	subgroup	G/H
center, hypercenter	C₅×C₁₃	D₉
commutator, cosocle, hypocenter	C₉	C₂×C₅×C₁₃
Frattini	C₃	C₅×D₃×C₁₃
Fitting	C₅×C₉×C₁₃	C₂
socle	C₃×C₅×C₁₃	D₃
LCS	G ▷ C₉
UCS	C₁ ◁ C₅×C₁₃

24 conjugacy classes of subgroups.

minimal degree	μ(G) = 27
transitive degree	μ_t(G) = 585

A minimal faithful permutation representation — 2 generators on 27 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);(20,27)(21,26)(22,25)(23,24)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1170, 8);