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C5×#5565 #11755950

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

Aliases

direct productC5×#5565

Splittings

FittingC3×C4×C5×D4 ⋊ C2
HallC3×C5 ⋊ #553
SylowC3 ⋊ C5×#553

Subgroups

subgroupG/H
centerC22×C5C23×D3
commutator, cosocleC22×C3C24×C5
FrattiniC22C23×C5×D3
FittingC3×C4×C5×D4C2
socleC22×C3×C5C24
hypercenterC4×C5×D4D3
hypocenterC3C5×#553
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C4×C5×D4

476 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)(17,20,21,19)(18,22,23,24);(10,14)(11,15)(18,23)(22,24);(9,11,12,15)(10,13,14,16)(17,19,21,20)(18,22,23,24);(7,8)(9,10)(11,13)(12,14)(15,16)(17,18)(19,22)(20,24)(21,23)

Conjugacy classes & character table

225 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×#83495, C5×#79441, #14458956, …
maximal normal subgroup ofC5×#83495, C5×#79441, #14458956, …
maximal quotient ofC5×#73457, C5×#73460, C5×#82335, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 10145);