Finite Group Databasebeta

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C3×D4×D15⋊D5 #72230746

order7200
automorphism?
homologyAbelianization (H1) = C24×C3 · Schur multiplier (H2) = C26

Aliases

direct productC3×D4×D15⋊D5

Splittings

FittingC32×C52×D4 ⋊ C22
HallC32×C52 ⋊ C22×D4
SylowC52 ⋊ C2×C3×D3×D4
SylowC32 ⋊ D4×D52

Subgroups

subgroupG/H
centerC2×C3C22×D15⋊D5
commutator, cosocleC2×C3×C52C24×C3
FrattiniC2C22×C3×D15⋊D5
FittingC32×C52×D4C22
socleC2×C32×C52C24
hypercenterC3×D4D15⋊D5
hypocenterC3×C52C22×C3×D4
LCSG ▷ C2×C3×C52 ▷ C3×C52
UCSC1 ◁ C2×C3 ◁ C3×D4

2320 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 120

Conjugacy classes & character table

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

GAP

Past the SmallGroups library coverage — no SmallGroups id.