C₅×#67003 #13183077

order	1760
isoclinism	isoclinic class of #4323
automorphism	?
homology	Abelianization (H₁) = C₂³×C₅ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₅×#67003

Splittings

Fitting	C₅×C₁₁×#41 ⋊ C₂
Hall	C₅×C₁₁ ⋊ #135
Sylow	C₁₁ ⋊ C₅×#135

Subgroups

	subgroup	G/H
center	C₄×C₅	C₂²⋊D₁₁
commutator, cosocle	C₄×C₁₁	C₂³×C₅
Frattini	C₄	C₂²×C₅×D₁₁
Fitting	C₅×C₁₁×#41	C₂
socle	C₂×C₅×C₁₁	C₂×D₄
hypercenter	C₅×#41	D₁₁
hypocenter	C₁₁	C₅×#135
LCS	G ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₄×C₅ ◁ C₂×C₄×C₅ ◁ C₅×#41

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

normal subgroups only

This group has 124 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)(20,28)(22,29)(24,25)(26,32)(30,31);(17,19,21,27)(18,22,25,31)(20,26,28,32)(23,29,24,30);(7,8)(9,10)(11,12)(13,14)(15,16)(17,18)(19,22)(20,23)(21,25)(24,28)(26,29)(27,31)(30,32)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1760, 886);