Finite Group Databasebeta

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C9×#16812514 #44533537

order31347
automorphism?
homologyAbelianization (H1) = C32×C9 · Schur multiplier (H2) = C33

Aliases

direct productC9×#16812514

Splittings

SylowC43 ⋊ C9×#733

Subgroups

subgroupG/H
centerC3×C9C32⋊(C43⋊C3)
commutatorC32×C43C32×C9
FrattiniC33C32×C43⋊C3
FittingC9×3−1+2×C43C3
socleC32×C43C3×H(3,𝔽3)
prime radical, cosocleC33×C43C33
hypercenterC9×3−1+2C43⋊C3
hypocenterC43C9×#733
LCSG ▷ C32×C43 ▷ C3×C43 ▷ C43
UCSC1 ◁ C3×C9 ◁ C32×C9 ◁ C9×3−1+2

274 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 274 conjugacy classes of subgroups — too many to draw. Only its 88 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) = 10449

Conjugacy classes & character table

1539 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31347, 2160);