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C5×#5806 #11756191

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

Aliases

direct productC5×#5806

Splittings

FittingC22×C3×C5×D4 ⋊ C2
HallC3×C5 ⋊ #546
SylowC3 ⋊ C5×#546

Subgroups

subgroupG/H
centerC22×C5C23×D3
commutator, cosocleC22×C3C24×C5
FrattiniC22C23×C5×D3
FittingC22×C3×C5×D4C2
socleC22×C3×C5C24
hypercenterC22×C5×D4D3
hypocenterC3C5×#546
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C22×C5×D4

668 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 20
transitive degreeμt(G) = 240

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

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

Conjugacy classes & character table

225 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×#80022, C5×#83837, #14453251, …
maximal normal subgroup ofC5×#80022, C5×#83837, #14453251, …
maximal quotient ofC5×D4×#217, C5×#82330, C5×#82098, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 10386);