C₅×C₁₇×C₁₃⋊C₃ #15693277

order	3315
isoclinism	isoclinic class of C₁₃⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₃×C₅×C₁₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₅×C₁₇×C₁₃⋊C₃
unambiguous semidirect product	C₁₃⋊(C₃×C₅×C₁₇)
unambiguous semidirect product	(C₅×C₁₃)⋊(C₃×C₁₇)
unambiguous semidirect product	(C₁₃×C₁₇)⋊(C₃×C₅)
unambiguous semidirect product	(C₅×C₁₃×C₁₇)⋊C₃

	subgroup	G/H
center, hypercenter	C₅×C₁₇	C₁₃⋊C₃
commutator, cosocle, hypocenter	C₁₃	C₃×C₅×C₁₇
Frattini	C₁	G
Fitting, socle	C₅×C₁₃×C₁₇	C₃
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₅×C₁₇

16 conjugacy classes of subgroups.

minimal degree	μ(G) = 35
transitive degree	μ_t(G) = 1105

A minimal faithful permutation representation — 2 generators on 35 points:

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3315, 2);