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C5×#5699 #11756084

order960
automorphism?
homologyAbelianization (H1) = C24×C5 · Schur multiplier (H2) = C24

Aliases

direct productC5×#5699

Splittings

FittingC3×C5×#125 ⋊ C2
HallC3×C5 ⋊ #563
SylowC3 ⋊ C5×#563

Subgroups

subgroupG/H
centerC22×C5C23×D3
commutator, cosocleC22×C3C24×C5
FrattiniC22C23×C5×D3
FittingC3×C5×#125C2
socleC22×C3×C5C24
prime radicalC2×C5×D12C22
hypercenterC5×#125D3
hypocenterC3C5×#563
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C5×#125

392 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 32
transitive degreeμt(G) = 480

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

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

Conjugacy classes & character table

165 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×#71249, C5×#68371, #14290963, …
maximal normal subgroup ofC5×#71249, C5×#68371, #14290963, …
maximal quotient ofC5×#75312, C5×#75992, C5×#75314, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 10279);