Finite Group Databasebeta

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Cayley diagram

C5×#874 #91677

order480
automorphism?
homologyAbelianization (H1) = C23×C5 · Schur multiplier (H2) = C22×C4

Aliases

direct productC5×#874

Splittings

FittingC3×C42×C5 ⋊ C2
HallC3×C5 ⋊ #127
SylowC3 ⋊ C5×#127

Subgroups

subgroupG/H
centerC22×C5C22×D3
commutator, cosocleC22×C3C23×C5
FrattiniC22C22×C5×D3
FittingC3×C42×C5C2
socleC22×C3×C5C23
hypercenterC42×C5D3
hypocenterC3C5×#127
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C42×C5

216 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 16
transitive degreeμt(G) = 240

A minimal faithful permutation representation — 3 generators on 16 points:

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

Conjugacy classes & character table

150 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11745853, C5×#4485, #11746901, …
maximal normal subgroup of#11745853, C5×#4485, #11746901, …
maximal quotient ofC5×#4671, C5×#4677, C5×#4693, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 753);