C₂²×C₃²×D₇ #92771

order	504
isoclinism	isoclinic class of D₇
automorphism	?
homology	Abelianization (H₁) = C₂³×C₃² · Schur multiplier (H₂) = C₂³×C₃

Aliases

C₂²×C₃²×D₇

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

192 conjugacy classes of subgroups.

minimal degree	μ(G) = 17
transitive degree	μ_t(G) = 252

A minimal faithful permutation representation — 3 generators on 17 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(504, 197);