Finite Group Databasebeta

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C5×D3×#711 #72259597

order2400
automorphism?
homologyAbelianization (H1) = C24×C5 · Schur multiplier (H2) = C25

Aliases

direct productC5×D3×#711

Splittings

FittingC3×C52×D4 ⋊ C22
HallC3×C52 ⋊ C2×#41
SylowC52 ⋊ D3×#41
SylowC3 ⋊ C2×C5×#711

Subgroups

subgroupG/H
centerC2×C5C22×D3×D5
commutator, cosocleC2×C3×C5C24×C5
FrattiniC2C22×C5×D3×D5
FittingC3×C52×D4C22
socleC2×C3×C52C24
hypercenterC5×D4D3×D5
hypocenterC3×C5C2×C5×#41
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C5 ◁ C5×D4

764 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 120

Conjugacy classes & character table

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

Relationships

maximal subgroup ofD3×#11717477
maximal normal subgroup ofD3×#11717477

GAP

Past the SmallGroups library coverage — no SmallGroups id.