Finite Group Databasebeta

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D3×#12763 #72271759

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

Aliases

direct productD3×#12763

Splittings

FittingC3×#12763 ⋊ C2
SylowC3 ⋊ C2×#12763

Subgroups

subgroupG/H
centerC22D3×B(4,𝔽2)
commutatorC2×C3×D4C23×C4
FrattiniC22×D4C23×D3
FittingC3×#12763C2
socleC22×C3C2×B(4,𝔽2)
prime radicalC2×D3×H(3,𝔽4)C2
cosocleC22×C3×D4C24
hypercenter#12763D3
hypocenterC3C2×#12763
LCSG ▷ C2×C3×D4 ▷ C22×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ #12763

6584 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 96

Conjugacy classes & character table

102 conjugacy classes — view the full character table.

Relationships

maximal quotient ofD3×#147779

GAP

Past the SmallGroups library coverage — no SmallGroups id.