C₅×#67004 #13183078

order	1760
automorphism	?
homology	Abelianization (H₁) = C₂³×C₅ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₅×#67004

Splittings

Hall	C₅×C₁₁ ⋊ #137
Sylow	C₁₁ ⋊ C₅×#137

Subgroups

	subgroup	G/H
center	C₂×C₅	C₂×C₂²⋊D₁₁
commutator, cosocle	C₄×C₁₁	C₂³×C₅
Frattini	C₄	C₂²×C₅×D₁₁
Fitting, prime radical	C₅×C₁₁×#41	C₂
socle	C₂×C₅×C₁₁	C₂×D₄
hypercenter	C₅×#41	D₁₁
hypocenter	C₁₁	C₅×#137
LCS	G ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₅ ◁ C₂×C₄×C₅ ◁ C₅×#41

120 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 58 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1760, 887);