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Cayley diagram

D5×C3⋊C16 #90931

order480
isoclinismisoclinic class of D3×D5
automorphism?
homologyAbelianization (H1) = C2×C16 · Schur multiplier (H2) = C2

Aliases

direct productD5×C3⋊C16

Splittings

derived, HallC3×C5 ⋊ C2×C16
SylowC5 ⋊ C2×C3⋊C16
SylowC3 ⋊ D5×C16

Subgroups

subgroupG/H
center, Frattini, hypercenterC8D3×D5
commutator, hypocenterC3×C5C2×C16
Fitting, cosocleC3×C5×C8C22
socleC2×C3×C5C2×C8
prime radicalC2×C3×D5C8
LCSG ▷ C3×C5
UCSC1 ◁ C8

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 2 generators on 24 points:

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

Conjugacy classes & character table

96 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽5)×C3⋊C16, ΓL(1,𝔽16)⋊C16, #11746450, …
maximal normal subgroup ofAGL(1,𝔽5)×C3⋊C16, ΓL(1,𝔽16)⋊C16, #11746450, …
maximal quotient ofD5×C3⋊C32, #11745815, Dic5×C3⋊C16, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 7);