Finite Group Databasebeta

← Prev (#10595450) Next (#10595452) →

D3×#949 #10595451

order576
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productD3×#949

Splittings

FittingC32×#41 ⋊ C22
SylowC32 ⋊ C2×AGL(1,ℤ/8)

Subgroups

subgroupG/H
centerC2C2×D3×#67
commutator, cosocleC32×C4C24
FrattiniC4C22×D32
FittingC32×#41C22
socleC2×C32C22×D4
hypercenter#41D32
hypocenterC32C2×AGL(1,ℤ/8)
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ #41

630 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 48

Conjugacy classes & character table

63 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×#4822, D3×#5241, D3×#4827, …
maximal normal subgroup ofD3×#4822, D3×#5241, D3×#4827, …
maximal quotient ofD3×#5001, D3×#5232, D3×#4995, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(576, 7333);