Finite Group Databasebeta

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D3×#12852 #72255131

order1536
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productD3×#12852

Splittings

FittingC3×#12852 ⋊ C2
SylowC3 ⋊ C2×#12852

Subgroups

subgroupG/H
centerC22C2×D3×#99
commutatorC24×C3C23×C4
FrattiniC22×D4C23×D3
FittingC3×#12852C2
socleC22×C3C22×#99
prime radicalC23×D3×D4C22
cosocleC22×C3×D4C24
hypercenter#12852D3
hypocenterC3C2×#12852
LCSG ▷ C24×C3 ▷ C22×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C24 ◁ C23×D4 ◁ #12852

6800 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 96

Conjugacy classes & character table

120 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×#496225, D3×#144415, D3×#144414, …
maximal normal subgroup ofD3×#496225, D3×#144415, D3×#144414, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.