Finite Group Databasebeta

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C3⋊D3×#65800 #72260116

order5760
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C29×C3

Aliases

direct productC3⋊D3×#65800

Splittings

FittingC24×C32×C5 ⋊ C2×C4
HallC32×C5 ⋊ C2×#379
SylowC32 ⋊ C2×#65800
SylowC5 ⋊ C3⋊D3×#379

Subgroups

subgroupG/H
center, FrattiniC22C22×C3⋊D3×AGL(1,𝔽5)
commutator, socleC22×C32×C5C23×C4
FittingC24×C32×C5C2×C4
prime radicalC24×D5×C3⋊D3C2
cosocleC22×C32×D5C24
hypercenterC24C3⋊D3×AGL(1,𝔽5)
hypocenterC32×C5C2×#379
LCSG ▷ C22×C32×C5 ▷ C32×C5
UCSC1 ◁ C22 ◁ C24

20784 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 360

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC3⋊D3×AGL(1,𝔽5)×#120
maximal normal subgroup ofC3⋊D3×AGL(1,𝔽5)×#120

GAP

Past the SmallGroups library coverage — no SmallGroups id.