Finite Group Databasebeta

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C5×#4546 #11746245

order960
isoclinismisoclinic class of #4537
automorphism?
homologyAbelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C2

Aliases

direct productC5×#4546

Splittings

HallC3×C5 ⋊ #333
SylowC3 ⋊ C5×#333

Subgroups

subgroupG/H
centerC22×C5#217
commutatorC2×C3×C4C2×C4×C5
FrattiniC42C2×C5×D3
FittingC3×C5×C4⋊Q8C2
socle, prime radicalC22×C3×C5C22⋊C4
cosocleC3×C42C22×C5
hypercenterC5×C4⋊Q8D3
hypocenterC3C5×#333
LCSG ▷ C2×C3×C4 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C42×C5 ◁ C5×C4⋊Q8

128 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 24
transitive degreeμt(G) = 960

A minimal faithful permutation representation — 2 generators on 24 points:

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

Conjugacy classes & character table

165 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×#67550, C5×#67773, #14279380, …
maximal normal subgroup ofC5×#67550, C5×#67773, #14279380, …
maximal quotient ofC5×#67642, C5×#67634, C5×#67800, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 440);