Finite Group Databasebeta

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D3×#2021 #10822415

order768
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C28

Aliases

direct productD3×#2021

Splittings

FittingC3×#2021 ⋊ C2
SylowC3 ⋊ C2×#2021

Subgroups

subgroupG/H
centerC22D3×#120
commutator, cosocleC24×C3C24
FrattiniC24C23×D3
FittingC3×#2021C2
socleC22×C3C2×#120
hypercenter#2021D3
hypocenterC3C2×#2021
LCSG ▷ C24×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C24 ◁ #2021

3986 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 48

Conjugacy classes & character table

78 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×#23900, C2×D3×#2021, D3×#73081, …
maximal normal subgroup ofD3×#23900, C2×D3×#2021, D3×#23895, …
maximal quotient ofD3×#10991, C2×D3×#2021, D3×#10336, …
automorphism group ofC4×C3⋊C8, #803

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(768, 196796);