Finite Group Databasebeta

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Cayley diagram

C22×D60 #92091

order480
isoclinismisoclinic class of Dic30
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct productC22×D60

Splittings

FittingC22×C3×C4×C5 ⋊ C2
HallC3×C5 ⋊ C22×D4
SylowC5 ⋊ C22×D12
SylowC3 ⋊ C22×D20

Subgroups

subgroupG/H
centerC23C2×D15
commutator, cosocleC2×C3×C5C24
FrattiniC2C23×D15
FittingC22×C3×C4×C5C2
socleC23×C3×C5C22
hypercenterC22×C4D15
hypocenterC3×C5C22×D4
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×C4

472 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 4 generators on 16 points:

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

Conjugacy classes & character table

132 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×#90960, C2×#90968, #11748392, …
maximal normal subgroup ofC2×#90960, C2×#90968, #11748392, …
maximal quotient ofC2×#91758, C2×C4×D60, C2×#91763, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 1167);