Finite Group Databasebeta

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Cayley diagram

C2×C5×D3×Q8 #92081

order480
automorphism?
homologyAbelianization (H1) = C24×C5 · Schur multiplier (H2) = C25

Aliases

direct productC2×C5×D3×Q8

Splittings

FittingC2×C3×C5×Q8 ⋊ C2
HallC3×C5 ⋊ C22×Q8
SylowC3 ⋊ C22×C5×Q8

Subgroups

subgroupG/H
centerC22×C5C22×D3
commutator, cosocleC2×C3C24×C5
FrattiniC2C23×C5×D3
FittingC2×C3×C5×Q8C2
socleC22×C3×C5C23
prime radicalC22×C5×D3C22
hypercenterC2×C5×Q8D3
hypocenterC3C22×C5×Q8
LCSG ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C2×C5×Q8

312 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 4 generators on 18 points:

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

Conjugacy classes & character table

150 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×#3967, #11749213, #11749278, …
maximal normal subgroup ofD3×#3967, #11749213, #11749278, …
maximal quotient ofC2×C5×#887, C2×C5×#888, C2×C5×#889, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 1157);