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C5×#5832 #11756217

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

Aliases

direct productC5×#5832

Splittings

FittingC2×C3×C5×#41 ⋊ C2
HallC3×C5 ⋊ #532
SylowC3 ⋊ C5×#532

Subgroups

subgroupG/H
centerC2×C4×C5C22×D3
commutator, cosocleC22×C3C24×C5
FrattiniC22C23×C5×D3
FittingC2×C3×C5×#41C2
socleC22×C3×C5C24
hypercenterC2×C5×#41D3
hypocenterC3C5×#532
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C2×C4×C5 ◁ C2×C5×#41

620 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)(15,19)(17,20);(13,15)(14,17)(16,19)(18,20);(13,14,16,18)(15,17,19,20);(7,8)(9,10)(11,12)(15,19)(17,20)

Conjugacy classes & character table

240 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×#70417, C5×#70045, C5×#72021, …
maximal normal subgroup ofC5×#70417, C5×#70045, C5×#72021, …
maximal quotient ofC5×#82224, C5×#82225, C5×#82228, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 10412);