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Cayley diagram

C5×(C2×D3)⋊C8 #91063

order480
isoclinismisoclinic class of Dic6
automorphism?
homologyAbelianization (H1) = C2×C5×C8 · Schur multiplier (H2) = C22

Aliases

direct productC5×(C2×D3)⋊C8
unambiguous semidirect product(C2×D3)⋊(C5×C8)

Splittings

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

Subgroups

subgroupG/H
centerC2×C4×C5C2×D3
commutatorC2×C3C2×C5×C8
FrattiniC2×C4C2×C5×D3
FittingC2×C3×C5×C8C2
socleC22×C3×C5C2×C4
prime radicalC22×C5×D3C4
cosocleC2×C3×C4C22×C5
hypercenterC2×C5×C8D3
hypocenterC3C5×C22⋊C8
LCSG ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C4×C5 ◁ C2×C5×C8

100 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 20
transitive degreeμt(G) = 240

A minimal faithful permutation representation — 2 generators on 20 points:

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

Conjugacy classes & character table

180 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11747579, #11747581, #11747591, …
maximal normal subgroup of#11747579, #11747581, #11747591, …
maximal quotient ofC5×#4456, C5×#4459, C5×#4468, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 139);