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C5×#5629 #11756014

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

Aliases

direct productC5×#5629

Splittings

FittingC3×C5×C22⋊Q8 ⋊ C2
HallC3×C5 ⋊ #537
SylowC3 ⋊ C5×#537

Subgroups

subgroupG/H
centerC22×C5C23×D3
commutator, cosocleC22×C3C24×C5
FrattiniC22C23×C5×D3
FittingC3×C5×C22⋊Q8C2
socleC22×C3×C5C24
hypercenterC5×C22⋊Q8D3
hypocenterC3C5×#537
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C5×C22⋊Q8

588 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)(16,19)(17,20);(9,10,11,12)(14,17)(15,19);(13,14,16,17)(15,18,19,20);(7,8)(15,19)(18,20)

Conjugacy classes & character table

180 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×#80149, C5×#80231, #14424701, …
maximal normal subgroup ofC5×#80149, C5×#80231, #14424701, …
maximal quotient ofC5×#74003, C5×#76482, C5×#76195, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 10209);