Finite Group Databasebeta

← Prev (#10948022) Next (#10948024) →

D3×#2134 #10948023

order768
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productD3×#2134

Splittings

FittingC3×#2134 ⋊ C2
SylowC3 ⋊ C2×#2134

Subgroups

subgroupG/H
centerC2C2×D3×#99
commutatorC2×C3×C4C23×C4
FrattiniC2×Q8C23×D3
FittingC3×#2134C2
socleC2×C3C22×#99
prime radicalD3×#535C2
cosocleC2×C3×Q8C24
hypercenter#2134D3
hypocenterC3C2×#2134
LCSG ▷ C2×C3×C4 ▷ C22×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#41 ◁ #2134

1390 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 48

Conjugacy classes & character table

69 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×#12711, D3×#33570, D3×#12755, …
maximal normal subgroup ofD3×#12711, D3×#33570, D3×#12755, …
maximal quotient ofC2×D3×#2134, D3×#12587

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(768, 322404);