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C5×#4952 #11750451

order960
isoclinismisoclinic class of #4656
automorphism?
homologyAbelianization (H1) = C23×C5 · Schur multiplier (H2) = C23

Aliases

direct productC5×#4952

Splittings

HallC3×C5 ⋊ #397
SylowC3 ⋊ C5×#397

Subgroups

subgroupG/H
centerC23×C5C22×D3
commutator, cosocleC23×C3C23×C5
FrattiniC23C22×C5×D3
FittingC2×C3×C5×C22⋊C4C2
socleC23×C3×C5C23
prime radicalC24×C3×C5C22
hypercenterC2×C5×C22⋊C4D3
hypocenterC3C5×#397
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23×C5 ◁ C2×C5×C22⋊C4

340 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 3 generators on 24 points:

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

Conjugacy classes & character table

210 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×D3×#397, C2×C5×#4952, D5×#4952, …
maximal normal subgroup ofC5×D3×#397, C2×C5×#4952, D5×#4952, …
maximal quotient ofC5×#71547, C5×#71549, C5×#71548, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 4646);