Finite Group Databasebeta

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C3×AGL(1,𝔽5)×(C2×D3)⋊C4 #72260261

order2880
automorphism?
homologyAbelianization (H1) = C2×C3×C42 · Schur multiplier (H2) = C23×C4

Aliases

direct productC3×AGL(1,𝔽5)×(C2×D3)⋊C4

Splittings

FittingC2×C32×C4×C5 ⋊ C2×C4
HallC32×C5 ⋊ C4×C22⋊C4
SylowC32 ⋊ C22⋊C4×AGL(1,𝔽5)
SylowC5 ⋊ C3×C4×(C2×D3)⋊C4

Subgroups

subgroupG/H
centerC22×C3C2×D3×AGL(1,𝔽5)
commutatorC2×C3×C5C2×C3×C42
FrattiniC22C2×C3×D3×AGL(1,𝔽5)
FittingC2×C32×C4×C5C2×C4
socleC22×C32×C5C22×C4
prime radicalC22×C3×D3×D5C22
cosocleC22×C3×D5C23×C3
hypercenterC2×C3×C4D3×AGL(1,𝔽5)
hypocenterC3×C5C3×C4×C22⋊C4
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22×C3 ◁ C2×C3×C4

1140 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 240

Conjugacy classes & character table

270 conjugacy classes. The character table is too large to display.

Relationships

maximal quotient ofC3×AGL(1,𝔽5)×#805

GAP

Past the SmallGroups library coverage — no SmallGroups id.