C₇²×D₅ #92440

order	490
isoclinism	isoclinic class of D₅
automorphism	?
homology	Abelianization (H₁) = C₂×C₇² · Schur multiplier (H₂) = C₇

Aliases

direct product	C₇²×D₅
unambiguous semidirect product	C₅⋊(C₂×C₇²)

Fitting, socle, Hall	C₅×C₇² ⋊ C₂
derived, Sylow	C₅ ⋊ C₂×C₇²

	subgroup	G/H
center, hypercenter	C₇²	D₅
commutator, cosocle, hypocenter	C₅	C₂×C₇²
Frattini	C₁	G
Fitting, socle	C₅×C₇²	C₂
LCS	G ▷ C₅
UCS	C₁ ◁ C₇²

40 conjugacy classes of subgroups.

minimal degree	μ(G) = 19
transitive degree	μ_t(G) = 245

A minimal faithful permutation representation — 2 generators on 19 points:

(2,3)(4,5)(13,14,15,16,17,18,19);(1,2,4,5,3)(6,7,8,9,10,11,12)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(490, 7);