Finite Group Databasebeta

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Cayley diagram

C5×D3×Q16 #91720

order480
automorphism?
homologyAbelianization (H1) = C23×C5 · Schur multiplier (H2) = C22

Aliases

direct productC5×D3×Q16

Splittings

FittingC3×C5×Q16 ⋊ C2
HallC3×C5 ⋊ C2×Q16
SylowC3 ⋊ C2×C5×Q16

Subgroups

subgroupG/H
centerC2×C5D3×D4
commutator, cosocleC3×C4C23×C5
FrattiniC4C22×C5×D3
FittingC3×C5×Q16C2
socleC2×C3×C5C2×D4
prime radicalC2×C5×D3D4
hypercenterC5×Q16D3
hypocenterC3C2×C5×Q16
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C5 ◁ C4×C5 ◁ C5×Q16

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 24
transitive degreeμt(G) = 240

A minimal faithful permutation representation — 3 generators on 24 points:

(1,3,5,11)(2,6,8,15)(4,13,14,10)(7,16,12,9)(17,18,19)(20,21,22,23,24);(1,2,5,8)(3,9,11,16)(4,12,14,7)(6,13,15,10);(18,19)

Conjugacy classes & character table

105 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×#3960, D3×#3961, #11748305, …
maximal normal subgroup ofD3×#3960, D3×#3961, #11748305, …
maximal quotient ofC5×#4790, C5×#4792, C5×#4793, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 796);