C₂²×C₃×C₁₃⋊C₃ #90872

order	468
isoclinism	isoclinic class of C₁₃⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃² · Schur multiplier (H₂) = C₂×C₃

Aliases

C₂²×C₃×C₁₃⋊C₃

	subgroup	G/H
center, hypercenter	C₂²×C₃	C₁₃⋊C₃
commutator, cosocle, hypocenter	C₁₃	C₂²×C₃²
Frattini	C₁	G
Fitting, socle	C₂²×C₃×C₁₃	C₃
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₂²×C₃

60 conjugacy classes of subgroups.

minimal degree	μ(G) = 20
transitive degree	μ_t(G) = 156

A minimal faithful permutation representation — 2 generators on 20 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(468, 47);