#99×C₁₃⋊C₃ #11928010

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

Aliases

direct product	#99×C₁₃⋊C₃
unambiguous semidirect product	(C₁₃×#99)⋊C₃

Fitting, Hall	C₁₃×#99 ⋊ C₃
Sylow	C₁₃ ⋊ C₃×#99

104 conjugacy classes of subgroups.

minimal degree	μ(G) = 21
transitive degree	μ_t(G) = 104

A minimal faithful permutation representation — 2 generators on 21 points:

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

maximal subgroup of	#99×D₁₃⋊C₃, C₁₃⋊C₃×B(4,𝔽₂), #72259180
maximal normal subgroup of	#99×D₁₃⋊C₃, C₁₃⋊C₃×B(4,𝔽₂), #72259180

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1248, 122);