Finite Group Databasebeta

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C5×#5551 #11755936

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

Aliases

direct productC5×#5551

Splittings

FittingC3×C4×C5×D4 ⋊ C2
HallC3×C5 ⋊ #547
SylowC3 ⋊ C5×#547

Subgroups

subgroupG/H
centerC22×C5C23×D3
commutator, cosocleC22×C3C24×C5
FrattiniC22C23×C5×D3
FittingC3×C4×C5×D4C2
socleC22×C3×C5C24
hypercenterC4×C5×D4D3
hypocenterC3C5×#547
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C4×C5×D4

584 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)(14,18)(17,20);(10,12)(13,15,16,19)(14,17,18,20);(9,10,11,12);(7,8)(13,14)(15,17)(16,18)(19,20)

Conjugacy classes & character table

225 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×#71012, C5×#68180, #14289138, …
maximal normal subgroup ofC5×#71012, C5×#68180, #14289138, …
maximal quotient ofC5×#73573, C5×#73767, C5×C4⋊C4×D12, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 10131);