Finite Group Databasebeta

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Cayley diagram

C4×D3×Dic5 #91397

order480
isoclinismisoclinic class of D3×D5
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4

Aliases

direct productC4×D3×Dic5

Splittings

derived, HallC3×C5 ⋊ C2×C42
SylowC5 ⋊ C42×D3
SylowC3 ⋊ C2×C4×Dic5

Subgroups

subgroupG/H
center, hypercenterC2×C4D3×D5
commutator, hypocenterC3×C5C2×C42
FrattiniC22C2×D3×D5
FittingC2×C3×C4×C5C22
socle, cosocleC22×C3×C5C23
prime radicalC22×C5×D3C22
LCSG ▷ C3×C5
UCSC1 ◁ C2×C4

216 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 16
transitive degreeμt(G) = 240

A minimal faithful permutation representation — 3 generators on 16 points:

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

Conjugacy classes & character table

96 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×C8×Dic5, #11747579, D3×#3946, …
maximal normal subgroup ofD3×C8×Dic5, #11747579, D3×#3946, …
maximal quotient ofC4×D3×#168, #11746977, D3×#3935, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 473);