C₂×C₃×D₃×D₇ #92763

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

Aliases

C₂×C₃×D₃×D₇

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

138 conjugacy classes of subgroups.

minimal degree	μ(G) = 15
transitive degree	μ_t(G) = 84

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(504, 189);