C₂×#41×C₁₃⋊C₃ #11929249

order	1248
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃ · Schur multiplier (H₂) = C₂⁵

Aliases

Fitting, Hall	C₂×C₁₃×#41 ⋊ C₃
Sylow	C₁₃ ⋊ C₂×C₃×#41

328 conjugacy classes of subgroups.

minimal degree	μ(G) = 23
transitive degree	μ_t(G) = 208

A minimal faithful permutation representation — 4 generators on 23 points:

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

maximal subgroup of	C₂×#41×D₁₃⋊C₃, C₂×#11929141, C₂×H(5,𝔽₂)×C₁₃⋊C₃
maximal normal subgroup of	C₂×#41×D₁₃⋊C₃, C₂×#11929141, C₂×H(5,𝔽₂)×C₁₃⋊C₃

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1248, 1361);