C₂³×C₃×D₇ #66756

order	336
isoclinism	isoclinic class of D₇
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃ · Schur multiplier (H₂) = C₂⁶

Aliases

C₂³×C₃×D₇

	subgroup	G/H
center, hypercenter	C₂³×C₃	D₇
commutator, cosocle, hypocenter	C₇	C₂⁴×C₃
Frattini	C₁	G
Fitting, socle	C₂³×C₃×C₇	C₂
LCS	G ▷ C₇
UCS	C₁ ◁ C₂³×C₃

268 conjugacy classes of subgroups.

minimal degree	μ(G) = 16
transitive degree	μ_t(G) = 168

A minimal faithful permutation representation — 4 generators on 16 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(336, 225);