#102×C₁₃⋊C₃ #11928013

order	1248
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₄ · Schur multiplier (H₂) = C₂²

Aliases

direct product	#102×C₁₃⋊C₃
unambiguous semidirect product	(C₁₃×#102)⋊C₃

Fitting, Hall	C₁₃×#102 ⋊ C₃
Sylow	C₁₃ ⋊ C₃×#102

100 conjugacy classes of subgroups.

minimal degree	μ(G) = 25
transitive degree	μ_t(G) = 208

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

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

maximal subgroup of	#102×D₁₃⋊C₃, C₁₃⋊C₃×#442, #72276142
maximal normal subgroup of	#102×D₁₃⋊C₃, C₁₃⋊C₃×#442, #72276142

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1248, 125);