Finite Group Databasebeta

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D3×#926 #10594932

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

Aliases

direct productD3×#926

Splittings

SylowC32 ⋊ C2×#117

Subgroups

subgroupG/H
centerC2×C4C2×D32
commutatorC2×C32C23×C4
FrattiniC22C22×D32
FittingC22×C32×C4C22
socle, cosocleC22×C32C24
prime radicalC23×C3×D3C22
hypercenterC22×C4D32
hypocenterC32C2×#117
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4

698 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 96

Conjugacy classes & character table

108 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×#4531, D3×#4557, D3×#4523, …
maximal normal subgroup ofD3×#4531, D3×#4557, D3×#4523, …
maximal quotient ofD3×#4932, C4×D3×#217, C4×D3×C4⋊Dic3, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(576, 6814);