Finite Group Databasebeta

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D3×#2178 #10948583

order768
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productD3×#2178

Splittings

FittingC3×#2178 ⋊ C2
SylowC3 ⋊ C2×#2178

Subgroups

subgroupG/H
centerC8D3×D8
commutatorC3×C8C23×C4
FrattiniC2×C8C23×D3
FittingC3×#2178C2
socleC2×C3C2×C4×D8
prime radicalD3×#508C2
cosocleC2×C3×C8C24
hypercenter#2178D3
hypocenterC3C2×#2178
LCSG ▷ C3×C8 ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C8 ◁ C2×C8 ◁ C4×C8 ◁ #2178

662 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 96

Conjugacy classes & character table

132 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×#12046, D3×#33463, D3×#12047, …
maximal normal subgroup ofD3×#12046, D3×#33463, D3×#12047, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(768, 322964);