Finite Group Databasebeta

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Cayley diagram

C5×#833 #91076

order480
automorphism?
homologyAbelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C2

Aliases

direct productC5×#833

Splittings

HallC3×C5 ⋊ #100
SylowC3 ⋊ C5×#100

Subgroups

subgroupG/H
centerC2×C5#217
commutatorC22×C3C2×C4×C5
FrattiniC2×C4C2×C5×D3
Fitting, prime radicalC2×C3×C5×D4C2
socleC2×C3×C5C22⋊C4
cosocleC2×C3×C4C22×C5
hypercenterC2×C5×D4D3
hypocenterC3C5×#100
LCSG ▷ C22×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C5 ◁ C2×C4×C5 ◁ C2×C5×D4

92 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 16
transitive degreeμt(G) = 120

A minimal faithful permutation representation — 2 generators on 16 points:

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

Conjugacy classes & character table

105 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11745995, #11745998, #11746001, …
maximal normal subgroup of#11745995, #11745998, #11746001, …
maximal quotient ofC5×#4525, C5×#4530, C5×#4540, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 152);