Finite Group Databasebeta

← Prev (#72260191) Next (#72260193) →

C3×D5⋊#805 #72260192

order2880
automorphism?
homologyAbelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23

Aliases

direct productC3×D5⋊#805

Splittings

HallC32×C5 ⋊ C2×#104
SylowC32 ⋊ D5⋊#104
SylowC5 ⋊ C2×C3×#805

Subgroups

subgroupG/H
centerC3×C4(C2×D3)⋊AGL(1,𝔽5)
commutatorC3×C4×C5C22×C3×C4
FrattiniC4C2×C3×D3×AGL(1,𝔽5)
FittingC2×C32×C4×C5C2×C4
socleC2×C32×C5C2×C22⋊C4
prime radicalC3×D5×#235C2
cosocleC3×C4×D5C23×C3
hypercenterC2×C3×C4D3×AGL(1,𝔽5)
hypocenterC3×C5C2×C3×#104
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C3×C4 ◁ C2×C3×C4

788 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 120

Conjugacy classes & character table

234 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#72260231, C3×AGL(1,𝔽5)×#805, #72260286
maximal normal subgroup of#72260231, C3×AGL(1,𝔽5)×#805, #72260286

GAP

Past the SmallGroups library coverage — no SmallGroups id.