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C5×#5599 #11755984

order960
automorphism?
homologyAbelianization (H1) = C24×C5 · Schur multiplier (H2) = C25

Aliases

direct productC5×#5599

Splittings

FittingC3×C5×#121 ⋊ C2
HallC3×C5 ⋊ #550
SylowC3 ⋊ C5×#550

Subgroups

subgroupG/H
centerC22×C5C23×D3
commutator, cosocleC22×C3C24×C5
FrattiniC22C23×C5×D3
FittingC3×C5×#121C2
socleC22×C3×C5C24
hypercenterC5×#121D3
hypocenterC3C5×#550
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C5×#121

624 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 20
transitive degreeμt(G) = 480

A minimal faithful permutation representation — 4 generators on 20 points:

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

Conjugacy classes & character table

195 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×#80728, C5×#80013, C5×#80128, …
maximal normal subgroup ofC5×#80728, C5×#80013, C5×#80128, …
maximal quotient ofC5×#73877, C5×#76301, C5×#75981, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 10179);