C₂×C₃²×D₁₃ #90875

order	468
isoclinism	isoclinic class of D₁₃
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃² · Schur multiplier (H₂) = C₂×C₃

Aliases

C₂×C₃²×D₁₃

	subgroup	G/H
center, hypercenter	C₂×C₃²	D₁₃
commutator, cosocle, hypocenter	C₁₃	C₂²×C₃²
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₁₃	C₂
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₂×C₃²

60 conjugacy classes of subgroups.

minimal degree	μ(G) = 21
transitive degree	μ_t(G) = 234

A minimal faithful permutation representation — 2 generators on 21 points:

(1,2)(3,4,5)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21);(1,2)(6,7,8)(9,10,12,14,16,18,20,21,19,17,15,13,11)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(468, 50);