C₅×#67001 #13183075

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

Aliases

direct product

C₅×#67001

Splittings

Hall	C₅×C₁₁ ⋊ #131
Sylow	C₁₁ ⋊ C₅×#131

Subgroups

	subgroup	G/H
center	C₄×C₅	C₂²×D₁₁
commutator	C₂×C₁₁	C₂²×C₄×C₅
Frattini	C₄	C₂²×C₅×D₁₁
Fitting, prime radical	C₅×C₁₁×#41	C₂
socle	C₂×C₅×C₁₁	C₂²×C₄
cosocle	C₄×C₁₁	C₂³×C₅
hypercenter	C₅×#41	D₁₁
hypocenter	C₁₁	C₅×#131
LCS	G ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₄×C₅ ◁ C₅×#41

124 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 3 generators on 32 points:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1760, 884);

C5×#67001 #13183075