C₁₃×#126⋊C₃ #11928746

order	1248
isoclinism	isoclinic class of #126⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₁₃ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₁₃×#126⋊C₃
unambiguous semidirect product	#126⋊(C₃×C₁₃)

	subgroup	G/H
center, hypercenter	C₁₃	#126⋊C₃
commutator, cosocle, hypocenter	C₄²	C₂×C₃×C₁₃
Frattini	C₂²	C₂×A₄×C₁₃
Fitting	C₁₃×#126	C₃
socle	C₂²×C₁₃	C₂×A₄
LCS	G ▷ C₄²
UCS	C₁ ◁ C₁₃

40 conjugacy classes of subgroups.

minimal degree	μ(G) = 29
transitive degree	μ_t(G) = 208

A minimal faithful permutation representation — 2 generators on 29 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13)(15,23,24,19,16,26)(17,18,20)(21,22,25,29,27,28);(14,26,18,29)(15,23,22,16)(17,21,20,24)(19,28,27,25)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1248, 858);