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C5×#5511 #11755896

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

Aliases

direct productC5×#5511

Splittings

FittingC2×C3×C5×C4⋊C4 ⋊ C2
HallC3×C5 ⋊ #554
SylowC3 ⋊ C5×#554

Subgroups

subgroupG/H
centerC22×C5C23×D3
commutator, cosocleC22×C3C24×C5
FrattiniC22C23×C5×D3
FittingC2×C3×C5×C4⋊C4C2
socleC22×C3×C5C24
prime radicalC2×C5×#67C22
hypercenterC2×C5×C4⋊C4D3
hypocenterC3C5×#554
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C2×C5×C4⋊C4

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)(10,14)(13,16)(18,22)(21,24);(11,15)(13,16)(17,19,20,23)(18,21,22,24);(9,11,12,15)(10,13,14,16);(7,8)(9,10)(11,13)(12,14)(15,16)(17,18)(19,21)(20,22)(23,24)

Conjugacy classes & character table

225 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×#78758, C5×#81342, #14458478, …
maximal normal subgroup ofC5×#78758, C5×#81342, #14458478, …
maximal quotient ofC5×#73768, C5×#82160, C5×C4⋊C4×#67, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 10091);