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C3×D3×C4⋊AGL(1,𝔽5) #13088643

order1440
automorphism?
homologyAbelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23

Aliases

direct productC3×D3×C4⋊AGL(1,𝔽5)

Splittings

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

Subgroups

subgroupG/H
centerC2×C3C2×D3×AGL(1,𝔽5)
commutatorC2×C3×C5C22×C3×C4
FrattiniC2C2×C3×D3×AGL(1,𝔽5)
FittingC32×C4×C5C2×C4
socleC2×C32×C5C22×C4
prime radicalC2×C3×D3×D5C22
cosocleC2×C3×D5C23×C3
hypercenterC3×C4D3×AGL(1,𝔽5)
hypocenterC3×C5C2×C3×C4⋊C4
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C3 ◁ C3×C4

394 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 120

Conjugacy classes & character table

126 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×D3×D4×AGL(1,𝔽5), C3×#11756846, D3×#91921, …
maximal normal subgroup ofC3×D3×D4×AGL(1,𝔽5), C3×#11756846, D3×#91921, …
maximal quotient ofAGL(1,ℤ/9)×C4⋊AGL(1,𝔽5), C3×D3×#87832, C3×#13088407

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1440, 4960);