Finite Group Databasebeta

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C5×#5529 #11755914

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

Aliases

direct productC5×#5529

Splittings

FittingC3×C5×#117 ⋊ C2
HallC3×C5 ⋊ #552
SylowC3 ⋊ C5×#552

Subgroups

subgroupG/H
centerC22×C5C23×D3
commutator, cosocleC22×C3C24×C5
FrattiniC22C23×C5×D3
FittingC3×C5×#117C2
socleC22×C3×C5C24
prime radicalC2×C5×#67C22
hypercenterC5×#117D3
hypocenterC3C5×#552
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C5×#117

428 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)(17,19,20,23)(18,22,21,24);(9,11,12,15)(10,13,14,16)(18,21)(22,24);(17,18,20,21)(19,22,23,24);(7,8)(9,10)(11,13)(12,14)(15,16)

Conjugacy classes & character table

225 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×#78845, C5×#81381, #14458649, …
maximal normal subgroup ofC5×#78845, C5×#81381, #14458649, …
maximal quotient ofC5×#73416, C5×#73767, C5×#82239, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 10109);