D₇×Dic₅ #63302

order	280
isoclinism	isoclinic class of D₅×D₇
automorphism	?
homology	Abelianization (H₁) = C₂×C₄ · Schur multiplier (H₂) = C₂

Aliases

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₅×D₇
commutator, hypocenter	C₅×C₇	C₂×C₄
Fitting, socle, cosocle	C₂×C₅×C₇	C₂²
prime radical	C₂×C₅×D₇	C₂
LCS	G ▷ C₅×C₇
UCS	C₁ ◁ C₂

32 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 2 generators on 16 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(280, 7);