C₂³×C₁₃⋊C₃ #64639

order	312
isoclinism	isoclinic class of C₁₃⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₂³×C₃ · Schur multiplier (H₂) = C₂³

Aliases

C₂³×C₁₃⋊C₃

Fitting, socle, Hall	C₂³×C₁₃ ⋊ C₃
derived, Sylow	C₁₃ ⋊ C₂³×C₃

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

64 conjugacy classes of subgroups.

minimal degree	μ(G) = 19
transitive degree	μ_t(G) = 104

A minimal faithful permutation representation — 3 generators on 19 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(312, 55);