#106×C₁₃⋊C₃ #11928017

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

Aliases

direct product	#106×C₁₃⋊C₃
unambiguous semidirect product	(C₁₃×#106)⋊C₃

Fitting, Hall	C₁₃×#106 ⋊ C₃
Sylow	C₁₃ ⋊ C₃×#106

72 conjugacy classes of subgroups.

minimal degree	μ(G) = 25
transitive degree	μ_t(G) = 416

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

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

maximal subgroup of	#106×D₁₃⋊C₃, C₁₃⋊C₃×#442, #72276141
maximal normal subgroup of	#106×D₁₃⋊C₃, C₁₃⋊C₃×#442, #72276141

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1248, 129);