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H(3,𝔽3)×C43⋊C27 #44533509

order31347
automorphism?
homologyAbelianization (H1) = C32×C27 · Schur multiplier (H2) = C34

Aliases

direct productH(3,𝔽3)×C43⋊C27

Splittings

SylowC43 ⋊ C27×H(3,𝔽3)

Subgroups

subgroupG/H
center, FrattiniC3×C9C32×C43⋊C3
commutatorC3×C43C32×C27
FittingC9×H(3,𝔽3)×C43C3
socleC32×C43C32×C9
prime radicalC3×H(3,𝔽3)×C43C9
cosocleC3×C9×C43C33
hypercenterC9×H(3,𝔽3)C43⋊C3
hypocenterC43C27×H(3,𝔽3)
LCSG ▷ C3×C43 ▷ C43
UCSC1 ◁ C3×C9 ◁ C9×H(3,𝔽3)

292 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10449

Conjugacy classes & character table

1683 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31347, 2132);