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H(3,𝔽3)×C211⋊C3 #30685277

order17091
automorphism?
homologyAbelianization (H1) = C33 · Schur multiplier (H2) = C34

Aliases

direct productH(3,𝔽3)×C211⋊C3

Splittings

FittingH(3,𝔽3)×C211 ⋊ C3
SylowC211 ⋊ C3×H(3,𝔽3)

Subgroups

subgroupG/H
center, FrattiniC3C32×C211⋊C3
commutator, socle, cosocleC3×C211C33
FittingH(3,𝔽3)×C211C3
hypercenterH(3,𝔽3)C211⋊C3
hypocenterC211C3×H(3,𝔽3)
LCSG ▷ C3×C211 ▷ C211
UCSC1 ◁ C3 ◁ H(3,𝔽3)

112 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1899

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17091, 40);