D₇×D₁₅ #88301

order	420
isoclinism	isoclinic class of D₇×D₁₅
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

direct product	D₇×D₁₅
unambiguous semidirect product	(C₃×D₇)⋊D₅
unambiguous semidirect product	(C₅×D₇)⋊D₃

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₅×C₇	C₂²
LCS	G ▷ C₃×C₅×C₇
UCS	C₁

40 conjugacy classes of subgroups.

minimal degree	μ(G) = 15
transitive degree	μ_t(G) = 105

A minimal faithful permutation representation — 2 generators on 15 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(420, 26);