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Cayley diagram

C2×C5×D3×C8 #91702

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

Aliases

direct productC2×C5×D3×C8

Splittings

FittingC2×C3×C5×C8 ⋊ C2
derived, SylowC3 ⋊ C22×C5×C8
HallC3×C5 ⋊ C22×C8

Subgroups

subgroupG/H
center, hypercenterC2×C5×C8D3
commutator, hypocenterC3C22×C5×C8
FrattiniC4C22×C5×D3
FittingC2×C3×C5×C8C2
socleC22×C3×C5C2×C4
prime radicalC22×C5×D3C4
cosocleC3×C4C23×C5
LCSG ▷ C3
UCSC1 ◁ C2×C5×C8

152 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 18
transitive degreeμt(G) = 240

A minimal faithful permutation representation — 3 generators on 18 points:

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

Conjugacy classes & character table

240 conjugacy classes — view the full character table.

Relationships

maximal subgroup of(C2×D3)⋊#672, C5×(C2×D3)⋊C16, C2×D3×#672, …
maximal normal subgroup of(C2×D3)⋊#672, C5×(C2×D3)⋊C16, C2×D3×#672, …
maximal quotient ofC5×C8×Dic6, C4×C5×D3×C8, C5×#4685, …
automorphism group ofDic3×C41, C2×D3×C41, C22×C3×C41
outer automorphism group ofC22×C3×C41

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 778);