Finite Group Databasebeta

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#44531909

order31347
automorphism?
homologyAbelianization (H1) = C3×C9 · Schur multiplier (H2) = C32

Aliases

No aliases for this group.

Splittings

SylowC43 ⋊ #10624452

Subgroups

subgroupG/H
centerC33C32⋊(C43⋊C3)
commutatorC33×C43C3×C9
FrattiniC34C3×C43⋊C3
FittingC32×3−1+2×C43C3
socleC33×C43H(3,𝔽3)
prime radical, cosocleC34×C43C32
hypercenterC32×3−1+2C43⋊C3
hypocenterC43#10624452
LCSG ▷ C33×C43 ▷ C32×C43 ▷ C43
UCSC1 ◁ C33 ◁ C34 ◁ C32×3−1+2

350 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10449

Polycyclic presentation:

3^6,43|a^3=d,b^3=f,b^a=bc,c^a=ce,g^a=g^36,c^b=cf

Conjugacy classes & character table

1491 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31347, 532);