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Cayley diagram

C24×C5×D3 #92135

order480
isoclinismisoclinic class of D3
automorphism?
homologyAbelianization (H1) = C25×C5 · Schur multiplier (H2) = C210

Aliases

direct productC24×C5×D3
unambiguous semidirect productC3⋊(C25×C5)
unambiguous semidirect product(C2×C3)⋊(C24×C5)

Splittings

Fitting, socleC24×C3×C5 ⋊ C2
derived, SylowC3 ⋊ C25×C5
HallC3×C5 ⋊ C25

Subgroups

subgroupG/H
center, hypercenterC24×C5D3
commutator, cosocle, hypocenterC3C25×C5
FrattiniC1G
Fitting, socleC24×C3×C5C2
LCSG ▷ C3
UCSC1 ◁ C24×C5

1496 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 5 generators on 16 points:

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

Conjugacy classes & character table

240 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11749496, C5×#4955, C22×(C2×D3)⋊Dic5, …
maximal normal subgroup of#11749496, C5×#4955, C22×(C2×D3)⋊Dic5, …
maximal quotient ofC23×C5×Dic6, C23×C4×C5×D3, C23×C5×D12, …
automorphism group ofD3×C8×C11, C11×ΓL(1,𝔽25)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 1211);