C₂²×C₃×D₂₁ #92773

order	504
isoclinism	isoclinic class of D₂₁
automorphism	?
homology	Abelianization (H₁) = C₂³×C₃ · Schur multiplier (H₂) = C₂³

Aliases

C₂²×C₃×D₂₁

	subgroup	G/H
center, hypercenter	C₂²×C₃	D₂₁
commutator, cosocle, hypocenter	C₃×C₇	C₂³×C₃
Frattini	C₁	G
Fitting, socle	C₂²×C₃²×C₇	C₂
LCS	G ▷ C₃×C₇
UCS	C₁ ◁ C₂²×C₃

138 conjugacy classes of subgroups.

minimal degree	μ(G) = 17
transitive degree	μ_t(G) = 168

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(504, 199);