C₂×D₇×C₃⋊D₃ #92764

order	504
isoclinism	isoclinic class of D₇×C₃⋊D₃
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂³×C₃

Aliases

C₂×D₇×C₃⋊D₃

	subgroup	G/H
center, hypercenter	C₂	D₇×C₃⋊D₃
commutator, cosocle, hypocenter	C₃²×C₇	C₂³
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₇	C₂²
LCS	G ▷ C₃²×C₇
UCS	C₁ ◁ C₂

192 conjugacy classes of subgroups.

minimal degree	μ(G) = 15
transitive degree	μ_t(G) = 126

A minimal faithful permutation representation — 3 generators on 15 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(504, 190);