C₁₃×#127⋊C₃ #11928747

order	1248
isoclinism	isoclinic class of #127⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₁₃ · Schur multiplier (H₂) = C₄

Aliases

direct product	C₁₃×#127⋊C₃
unambiguous semidirect product	#127⋊(C₃×C₁₃)

	subgroup	G/H
center, hypercenter	C₁₃	#127⋊C₃
commutator, cosocle, hypocenter	C₄²	C₂×C₃×C₁₃
Frattini	C₂²	C₂×A₄×C₁₃
Fitting	C₁₃×#127	C₃
socle	C₂²×C₁₃	C₂×A₄
LCS	G ▷ C₄²
UCS	C₁ ◁ C₁₃

56 conjugacy classes of subgroups.

minimal degree	μ(G) = 25
transitive degree	μ_t(G) = 156

A minimal faithful permutation representation — 2 generators on 25 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1248, 859);