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C2×D3×#509 #11701676

order768
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productC2×D3×#509

Splittings

FittingC2×C3×#509 ⋊ C2
SylowC3 ⋊ C22×#509

Subgroups

subgroupG/H
centerC22C2×D3×D8
commutator, cosocleC3×C8C25
FrattiniC8C24×D3
FittingC2×C3×#509C2
socleC22×C3C22×D8
hypercenterC2×#509D3
hypocenterC3C22×#509
LCSG ▷ C3×C8 ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#509

2334 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 96

Conjugacy classes & character table

96 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×D3×AGL(1,ℤ/16), D3×#33517, D3×#13037, …
maximal normal subgroup ofC2×D3×AGL(1,ℤ/16), D3×#33517, D3×#13037, …
maximal quotient ofD3×#33517, C2×C3⋊D3×#509, D32×#509, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(768, 1076057);