#117×C₁₁⋊C₅ #13182589

order	1760
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₅ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product	#117×C₁₁⋊C₅
unambiguous semidirect product	(C₁₁×#117)⋊C₅

Fitting, Hall	C₁₁×#117 ⋊ C₅
Sylow	C₁₁ ⋊ C₅×#117

152 conjugacy classes of subgroups.

minimal degree	μ(G) = 23
transitive degree	μ_t(G) = 176

A minimal faithful permutation representation — 3 generators on 23 points:

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

maximal subgroup of	C₁₁⋊C₅×#525, #117×AGL(1,𝔽₁₁), #72248832, …
maximal normal subgroup of	C₁₁⋊C₅×#525, #117×AGL(1,𝔽₁₁), #72248832, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1760, 398);