Finite Group Databasebeta

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D3×#34290 #72255322

order1536
automorphism?
homologyAbelianization (H1) = C25×C4 · Schur multiplier (H2) = C214

Aliases

direct productD3×#34290

Splittings

FittingC3×#34290 ⋊ C2
SylowC3 ⋊ C2×#34290

Subgroups

subgroupG/H
center, FrattiniC23C25×D3
commutatorC22×C3C25×C4
FittingC3×#34290C2
socle, cosocleC23×C3C26
prime radicalC2×D3×D42C2
hypercenter#34290D3
hypocenterC3C2×#34290
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23 ◁ #34290

At least 7068 conjugacy classes of subgroups; only the 6731 normal subgroups are shown.

Full subgroup data →

Conjugacy classes & character table

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

Relationships

maximal subgroup ofD3×#7684106
maximal normal subgroup ofD3×#7684106
maximal quotient ofD3×#518019

GAP

Past the SmallGroups library coverage — no SmallGroups id.