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H(3,𝔽3)×C277⋊C3 #36376247

order22437
automorphism?
homologyAbelianization (H1) = C33 · Schur multiplier (H2) = C34

Aliases

direct productH(3,𝔽3)×C277⋊C3

Splittings

FittingH(3,𝔽3)×C277 ⋊ C3
SylowC277 ⋊ C3×H(3,𝔽3)

Subgroups

subgroupG/H
center, FrattiniC3C32×C277⋊C3
commutator, socle, cosocleC3×C277C33
FittingH(3,𝔽3)×C277C3
hypercenterH(3,𝔽3)C277⋊C3
hypocenterC277C3×H(3,𝔽3)
LCSG ▷ C3×C277 ▷ C277
UCSC1 ◁ C3 ◁ H(3,𝔽3)

112 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2493

Conjugacy classes & character table

1045 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22437, 40);