C₂×D₅×D₇ #63331

order	280
isoclinism	isoclinic class of D₅×D₇
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂³

Aliases

direct product	C₂×D₅×D₇
unambiguous semidirect product	(C₇×D₅)⋊C₂²
unambiguous semidirect product	(C₅×D₇)⋊C₂²
unambiguous semidirect product	D₃₅⋊C₂²

	subgroup	G/H
center, hypercenter	C₂	D₅×D₇
commutator, cosocle, hypocenter	C₅×C₇	C₂³
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₇	C₂²
LCS	G ▷ C₅×C₇
UCS	C₁ ◁ C₂

64 conjugacy classes of subgroups.

minimal degree	μ(G) = 14
transitive degree	μ_t(G) = 70

A minimal faithful permutation representation — 3 generators on 14 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(280, 36);