C₁₁×#4150 #13183437

order	1760
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₁ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₁₁×#4150

Splittings

Fitting	C₅×C₁₁×#41 ⋊ C₂
Hall	C₅×C₁₁ ⋊ 2₋¹⁺⁴
Sylow	C₅ ⋊ C₁₁×2₋¹⁺⁴

Subgroups

	subgroup	G/H
center	C₂×C₁₁	C₂³×D₅
commutator, cosocle	C₂×C₅	C₂⁴×C₁₁
Frattini	C₂	C₂³×D₅×C₁₁
Fitting	C₅×C₁₁×#41	C₂
socle	C₂×C₅×C₁₁	C₂⁴
hypercenter	C₁₁×#41	D₅
hypocenter	C₅	C₁₁×2₋¹⁺⁴
LCS	G ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₁₁ ◁ C₁₁×#41

292 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 32
transitive degree	μ_t(G) = 880

A minimal faithful permutation representation — 4 generators on 32 points:

(1,2,3,4,5,6,7,8,9,10,11)(12,13,15,16,14)(17,21,22,20)(18,24,25,29)(19,26,27,28)(23,31,32,30);(17,20,22,21)(18,24,25,29)(19,26,27,28)(23,30,32,31);(17,19,22,27)(18,23,25,32)(20,28,21,26)(24,31,29,30);(13,14)(15,16)(17,18)(19,23)(20,24)(21,29)(22,25)(26,30)(27,32)(28,31)

Conjugacy classes & character table

407 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1760, 1246);

C11×#4150 #13183437