Finite Group Databasebeta

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Cayley diagram

C5×#940 #91743

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

Aliases

direct productC5×#940

Splittings

FittingC2×C3×C5×D4 ⋊ C2
HallC3×C5 ⋊ #127
SylowC3 ⋊ C5×#127

Subgroups

subgroupG/H
centerC22×C5C22×D3
commutator, cosocleC22×C3C23×C5
FrattiniC22C22×C5×D3
FittingC2×C3×C5×D4C2
socleC22×C3×C5C23
hypercenterC2×C5×D4D3
hypocenterC3C5×#127
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C2×C5×D4

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

Conjugacy classes & character table

120 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11746007, C5×#4474, #11748941, …
maximal normal subgroup of#11746007, C5×#4474, #11748941, …
maximal quotient ofC5×#4949, C5×#4957, C5×#4960, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 819);