Finite Group Databasebeta

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C5×#5829 #11756214

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

Aliases

direct productC5×#5829

Splittings

FittingC2×C3×C5×#41 ⋊ C2
HallC3×C5 ⋊ #546
SylowC3 ⋊ C5×#546

Subgroups

subgroupG/H
centerC22×C5C23×D3
commutator, cosocleC22×C3C24×C5
FrattiniC22C23×C5×D3
FittingC2×C3×C5×#41C2
socleC22×C3×C5C24
hypercenterC2×C5×#41D3
hypocenterC3C5×#546
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C2×C5×#41

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

Conjugacy classes & character table

225 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×#83952, C5×#80120, #14453229, …
maximal normal subgroup ofC5×#83952, C5×#80120, #14453229, …
maximal quotient ofC5×D4×(C2×D3)⋊C4, C5×#84088, C5×#82271, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 10409);