Finite Group Databasebeta

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C5×#5658 #11756043

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

Aliases

direct productC5×#5658

Splittings

FittingC3×C5×#123 ⋊ C2
HallC3×C5 ⋊ #551
SylowC3 ⋊ C5×#551

Subgroups

subgroupG/H
centerC22×C5C23×D3
commutator, cosocleC22×C3C24×C5
FrattiniC22C23×C5×D3
FittingC3×C5×#123C2
socleC22×C3×C5C24
prime radicalC5×#937C2
hypercenterC5×#123D3
hypocenterC3C5×#551
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C5×#123

496 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 24
transitive degreeμt(G) = 240

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

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

Conjugacy classes & character table

195 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×D3×#551, C2×C5×#5658, D5×#5658, …
maximal normal subgroup ofC5×D3×#551, C2×C5×#5658, D5×#5658, …
maximal quotient ofC5×#74122, C5×#74595, C5×#75303, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 10238);