Finite Group Databasebeta

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D3×#877 #10594047

order576
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4

Aliases

direct productD3×#877

Splittings

SylowC32 ⋊ C2×#117

Subgroups

subgroupG/H
center, FrattiniC22C22×D32
commutatorC2×C32C23×C4
FittingC32×C22⋊C4C22
socle, cosocleC22×C32C24
prime radicalC23×C3×D3C22
hypercenterC22⋊C4D32
hypocenterC32C2×#117
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22⋊C4

698 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 96

Conjugacy classes & character table

90 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×#4740, D32×#117, C2×D3×#877, …
maximal normal subgroup ofD3×#4740, D32×#117, C2×D3×#877, …
maximal quotient ofD3×#4648, D3×Dic3×C22⋊C4, D3×#4649, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(576, 5929);