C₂²×C₇×C₃⋊D₃ #92774

order	504
isoclinism	isoclinic class of C₃⋊D₃
automorphism	?
homology	Abelianization (H₁) = C₂³×C₇ · Schur multiplier (H₂) = C₂³×C₃

Aliases

C₂²×C₇×C₃⋊D₃

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(504, 200);