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C3×C4×D3×AGL(1,𝔽5) #13088641

order1440
isoclinismisoclinic class of D3×AGL(1,𝔽5)
automorphism?
homologyAbelianization (H1) = C2×C3×C42 · Schur multiplier (H2) = C22×C4

Aliases

direct productC3×C4×D3×AGL(1,𝔽5)

Splittings

FittingC32×C4×C5 ⋊ C2×C4
derivedC3×C5 ⋊ C2×C3×C42
HallC32×C5 ⋊ C2×C42
SylowC32 ⋊ C2×C4×AGL(1,𝔽5)
SylowC5 ⋊ C3×C42×D3

Subgroups

subgroupG/H
center, hypercenterC3×C4D3×AGL(1,𝔽5)
commutator, hypocenterC3×C5C2×C3×C42
FrattiniC2C2×C3×D3×AGL(1,𝔽5)
FittingC32×C4×C5C2×C4
socleC2×C32×C5C22×C4
prime radicalC2×C3×D3×D5C22
cosocleC2×C3×D5C23×C3
LCSG ▷ C3×C5
UCSC1 ◁ C3×C4

462 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 120

Conjugacy classes & character table

180 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×D3×D4×AGL(1,𝔽5), C3×AGL(1,𝔽5)×#237, D3×AGL(1,𝔽5)×D12, …
maximal normal subgroup ofC3×D3×D4×AGL(1,𝔽5), C3×AGL(1,𝔽5)×#237, D3×AGL(1,𝔽5)×D12, …
maximal quotient ofC3×D3×AGL(1,𝔽5)2, C4×AGL(1,𝔽5)×AGL(1,ℤ/9), C3×D3×#87830, …
automorphism group ofC13×D15

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1440, 4958);