C₂²×D₆₃ #92639

order	504
isoclinism	isoclinic class of D₆₃
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂³

Aliases

C₂²×D₆₃

	subgroup	G/H
center, hypercenter	C₂²	D₆₃
commutator, cosocle, hypocenter	C₇×C₉	C₂³
Frattini	C₃	C₂²×D₂₁
Fitting	C₂²×C₇×C₉	C₂
socle	C₂²×C₃×C₇	D₃
LCS	G ▷ C₇×C₉
UCS	C₁ ◁ C₂²

96 conjugacy classes of subgroups.

minimal degree	μ(G) = 20
transitive degree	μ_t(G) = 252

A minimal faithful permutation representation — 3 generators on 20 points:

(1,2)(3,4)(6,7)(8,9)(10,11)(13,15)(14,18)(16,17)(19,20);(3,4)(5,6,8,10,11,9,7)(12,20,15,18,17,16,14,13,19);(1,2)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(504, 65);