Finite Group Databasebeta

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D3×#1782 #10794311

order768
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C29

Aliases

direct productD3×#1782

Splittings

FittingC3×#1782 ⋊ C2
SylowC3 ⋊ C2×#1782

Subgroups

subgroupG/H
centerC22C2×D3×C22⋊C4
commutatorC23×C3C23×C4
FrattiniC24C23×D3
FittingC3×#1782C2
socleC22×C3C22×C22⋊C4
prime radicalC22×D3×#41C2
cosocleC24×C3C24
hypercenter#1782D3
hypocenterC3C2×#1782
LCSG ▷ C23×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1782

4062 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 96

Conjugacy classes & character table

96 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×#23896, D3×#20584, D3×#23902, …
maximal normal subgroup ofD3×#23896, D3×#20584, D3×#23902, …
maximal quotient ofD3×#10980, D3×#8542, D3×#12725, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(768, 168692);