C₁₃×#95⋊C₃ #11928025

order	1248
isoclinism	isoclinic class of #95⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₃×C₁₃ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₁₃×#95⋊C₃
unambiguous semidirect product	#95⋊(C₃×C₁₃)

Fitting, Hall	C₁₃×#95 ⋊ C₃
derived, Sylow	#95 ⋊ C₃×C₁₃

	subgroup	G/H
center, hypercenter	C₂×C₁₃	C₄²⋊C₃
commutator, cosocle, hypocenter	#95	C₃×C₁₃
Frattini	C₂³	A₄×C₁₃
Fitting	C₁₃×#95	C₃
socle	C₂³×C₁₃	A₄
LCS	G ▷ #95
UCS	C₁ ◁ C₂×C₁₃

42 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)(16,20,25)(17,21,24)(19,23,22);(14,16,17,22)(18,23)(19,20)(24,25)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1248, 137);