C₂²×C₇×D₅ #63333

order	280
isoclinism	isoclinic class of D₅
automorphism	?
homology	Abelianization (H₁) = C₂³×C₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product	C₂²×C₇×D₅
unambiguous semidirect product	C₅⋊(C₂³×C₇)
unambiguous semidirect product	(C₂×C₅)⋊(C₂²×C₇)

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

64 conjugacy classes of subgroups.

minimal degree	μ(G) = 16
transitive degree	μ_t(G) = 140

A minimal faithful permutation representation — 3 generators on 16 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(280, 38);