C₅×#67043 #13183422

order	1760
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₅ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₅×#67043

Splittings

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

Subgroups

	subgroup	G/H
center	C₂×C₅	C₂³×D₁₁
commutator, cosocle	C₂×C₁₁	C₂⁴×C₅
Frattini	C₂	C₂³×C₅×D₁₁
Fitting	C₅×C₁₁×#41	C₂
socle	C₂×C₅×C₁₁	C₂⁴
hypercenter	C₅×#41	D₁₁
hypocenter	C₁₁	C₅×2₋¹⁺⁴
LCS	G ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₅ ◁ C₅×#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)(6,7,9,11,13,15,16,14,12,10,8)(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);(7,8)(9,10)(11,12)(13,14)(15,16)(17,18)(19,23)(20,24)(21,29)(22,25)(26,30)(27,32)(28,31)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1760, 1231);

C5×#67043 #13183422