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C22×D3×#124 #11701847

order768
automorphism?
homologyAbelianization (H1) = C26 · Schur multiplier (H2) = C213×C4

Aliases

direct productC22×D3×#124

Splittings

FittingC22×C3×#124 ⋊ C2
SylowC3 ⋊ C23×#124

Subgroups

subgroupG/H
centerC24C23×D3
commutator, cosocleC22×C3C26
FrattiniC22C25×D3
FittingC22×C3×#124C2
socleC24×C3C24
prime radicalC23×D3×D4C2
hypercenterC22×#124D3
hypocenterC3C23×#124
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C24 ◁ C22×#124

14334 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 192

Conjugacy classes & character table

168 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×#14662, D3×#14169, D3×#14473, …
maximal normal subgroup ofD3×#14662, D3×#14169, D3×#14473, …
maximal quotient ofD3×#60619

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(768, 1076228);