Finite Group Databasebeta

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Cayley diagram

C5×#834 #91077

order480
automorphism?
homologyAbelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C22

Aliases

direct productC5×#834

Splittings

HallC3×C5 ⋊ #99
SylowC3 ⋊ C5×#99

Subgroups

subgroupG/H
centerC2×C5#217
commutatorC22×C3C2×C4×C5
FrattiniC23C2×C5×D3
Fitting, prime radicalC2×C3×C5×D4C2
socleC2×C3×C5C22⋊C4
cosocleC23×C3C22×C5
hypercenterC2×C5×D4D3
hypocenterC3C5×#99
LCSG ▷ C22×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C5 ◁ C23×C5 ◁ C2×C5×D4

104 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)(4,6)(5,8)(7,11)(9,10)(12,13,14,15,16);(2,3)(4,5)(6,10,11,8)(7,9)

Conjugacy classes & character table

105 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11745994, #11745999, #11746000, …
maximal normal subgroup of#11745994, #11745999, #11746000, …
maximal quotient ofC5×#4525, C5×#4526, C5×#4528, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 153);