C₂²×C₃×D₁₃ #64642

order	312
isoclinism	isoclinic class of D₁₃
automorphism	?
homology	Abelianization (H₁) = C₂³×C₃ · Schur multiplier (H₂) = C₂³

Aliases

C₂²×C₃×D₁₃

	subgroup	G/H
center, hypercenter	C₂²×C₃	D₁₃
commutator, cosocle, hypocenter	C₁₃	C₂³×C₃
Frattini	C₁	G
Fitting, socle	C₂²×C₃×C₁₃	C₂
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₂²×C₃

64 conjugacy classes of subgroups.

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

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(312, 58);