C₇×(C₃⋊D₃)⋊D₅ #11929562

order	1260
isoclinism	isoclinic class of (C₃⋊D₃)⋊D₅
automorphism	?
homology	Abelianization (H₁) = C₂²×C₇ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₇×(C₃⋊D₃)⋊D₅
unambiguous semidirect product	(C₃⋊D₃)⋊(C₇×D₅)
unambiguous semidirect product	D₁₅⋊(D₃×C₇)

	subgroup	G/H
center, hypercenter	C₇	(C₃⋊D₃)⋊D₅
commutator, cosocle, hypocenter	C₃²×C₅	C₂²×C₇
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₇	C₂²
LCS	G ▷ C₃²×C₅
UCS	C₁ ◁ C₇

88 conjugacy classes of subgroups.

minimal degree	μ(G) = 18
transitive degree	μ_t(G) = 210

A minimal faithful permutation representation — 2 generators on 18 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1260, 114);