Finite Group Databasebeta

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C9×C3⋊#272 #13091364

order1458
automorphism?
homologyAbelianization (H1) = C2×C9 · Schur multiplier (H2) = C32

Aliases

direct productC9×C3⋊#272
unambiguous semidirect productC3⋊(C9×#272)

Splittings

Fitting, SylowC3×C9×H(3,𝔽3) ⋊ C2
derivedC3×H(3,𝔽3) ⋊ C2×C9

Subgroups

subgroupG/H
center, hypercenterC3×C9C3⋊(C3⋊D3)
commutator, hypocenterC3×H(3,𝔽3)C2×C9
FrattiniC32C3×C3⋊(C3⋊D3)
FittingC3×C9×H(3,𝔽3)C2
socleC33C3×C3⋊D3
prime radicalC3×C3⋊#272C3
cosocleC32×H(3,𝔽3)C2×C3
LCSG ▷ C3×H(3,𝔽3)
UCSC1 ◁ C3×C9

737 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 737 conjugacy classes of subgroups — too many to draw. Only its 101 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 162

Conjugacy classes & character table

189 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1458, 1438);