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C5×#5730 #11756115

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

Aliases

direct productC5×#5730

Splittings

FittingC3×C5×C4⋊Q8 ⋊ C2
HallC3×C5 ⋊ #554
SylowC3 ⋊ C5×#554

Subgroups

subgroupG/H
centerC22×C5C23×D3
commutator, cosocleC22×C3C24×C5
FrattiniC22C23×C5×D3
FittingC3×C5×C4⋊Q8C2
socleC22×C3×C5C24
prime radicalC2×C5×D12C22
hypercenterC5×C4⋊Q8D3
hypocenterC3C5×#554
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C5×C4⋊Q8

456 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 24
transitive degreeμt(G) = 480

A minimal faithful permutation representation — 4 generators on 24 points:

(1,2,3,4,5)(6,7,8)(9,11)(10,14)(12,16)(13,15)(17,19,20,24)(18,22,21,23);(9,11,12,16)(10,14,15,13);(9,11,12,16)(10,13,15,14)(17,18,20,21)(19,23,24,22);(7,8)(9,10)(11,14)(12,15)(13,16)(18,21)(22,23)

Conjugacy classes & character table

195 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×#71264, C5×#68490, #14288973, …
maximal normal subgroup ofC5×#71264, C5×#68490, #14288973, …
maximal quotient ofC5×#76201, C5×#74360, C5×#76203, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 10310);