Finite Group Databasebeta

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C2×D3×#568 #11708949

order768
automorphism?
homologyAbelianization (H1) = C25×C4 · Schur multiplier (H2) = C214

Aliases

direct productC2×D3×#568

Splittings

FittingC2×C3×#568 ⋊ C2
SylowC3 ⋊ C22×#568

Subgroups

subgroupG/H
centerC2×C4C24×D3
commutatorC2×C3C25×C4
FrattiniC4C25×D3
FittingC2×C3×#568C2
socleC22×C3C24×C4
prime radicalC22×D3×#41C2
cosocleC3×C4C26
hypercenterC2×#568D3
hypocenterC3C22×#568
LCSG ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C4 ◁ C2×#568

11118 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 96

Conjugacy classes & character table

204 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×D3×#1910, D3×#10742, D3×#10751, …
maximal normal subgroup ofC2×D3×#1910, D3×#10742, D3×#10751, …
maximal quotient ofD3×#60207, D3×#60208, D3×#60141, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(768, 1083330);