Finite Group Databasebeta

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Cayley diagram

C22×C5×C3⋊C8 #91723

order480
isoclinismisoclinic class of D3
automorphism?
homologyAbelianization (H1) = C22×C5×C8 · Schur multiplier (H2) = C23

Aliases

direct productC22×C5×C3⋊C8

Splittings

derived, SylowC3 ⋊ C22×C5×C8
HallC3×C5 ⋊ C22×C8

Subgroups

subgroupG/H
center, hypercenterC22×C4×C5D3
commutator, hypocenterC3C22×C5×C8
FrattiniC4C22×C5×D3
FittingC22×C3×C4×C5C2
socle, prime radicalC23×C3×C5C4
cosocleC3×C4C23×C5
LCSG ▷ C3
UCSC1 ◁ C22×C4×C5

152 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 20
transitive degreeμt(G) = 480

A minimal faithful permutation representation — 3 generators on 20 points:

(1,2)(3,4)(6,7)(8,9,10,11,12)(13,14,15,17,16,18,19,20);(3,4)(5,6,7);(1,2)

Conjugacy classes & character table

240 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11745966, #11745968, #11745980, …
maximal normal subgroup of#11745966, #11745968, #11745980, …
maximal quotient ofC2×C4×C5×C3⋊C8, C2×C5×C4⋊(C3⋊C8), C5×#4925, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 799);