C₃²×C₅⋊D₃₅ #15691305

order	3150
isoclinism	isoclinic class of C₅⋊D₃₅
automorphism	?
homology	Abelianization (H₁) = C₂×C₃² · Schur multiplier (H₂) = C₃×C₅

Aliases

direct product	C₃²×C₅⋊D₃₅
unambiguous semidirect product	C₅⋊(C₃²×D₃₅)

	subgroup	G/H
center, hypercenter	C₃²	C₅⋊D₃₅
commutator, cosocle, hypocenter	C₅²×C₇	C₂×C₃²
Frattini	C₁	G
Fitting, socle	C₃²×C₅²×C₇	C₂
LCS	G ▷ C₅²×C₇
UCS	C₁ ◁ C₃²

192 conjugacy classes of subgroups.

minimal degree	μ(G) = 23
transitive degree	μ_t(G) = 1575

A minimal faithful permutation representation — 3 generators on 23 points:

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3150, 104);