C₇×C₅⋊D₅ #66842

order	350
isoclinism	isoclinic class of C₅⋊D₅
automorphism	?
homology	Abelianization (H₁) = C₂×C₇ · Schur multiplier (H₂) = C₅

Aliases

direct product	C₇×C₅⋊D₅
unambiguous semidirect product	C₅⋊(C₇×D₅)

Fitting, socle, Hall	C₅²×C₇ ⋊ C₂
derived, Sylow	C₅² ⋊ C₂×C₇

	subgroup	G/H
center, hypercenter	C₇	C₅⋊D₅
commutator, cosocle, hypocenter	C₅²	C₂×C₇
Frattini	C₁	G
Fitting, socle	C₅²×C₇	C₂
LCS	G ▷ C₅²
UCS	C₁ ◁ C₇

32 conjugacy classes of subgroups.

minimal degree	μ(G) = 17
transitive degree	μ_t(G) = 175

A minimal faithful permutation representation — 3 generators on 17 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(350, 8);