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C3×#10620012 #14519050

order1944
automorphism?
homologyAbelianization (H1) = C32 · Schur multiplier (H2) = C3

Aliases

direct productC3×#10620012

Subgroups

subgroupG/H
center, socle, hypercenterC32PSU(3,𝔽2)⋊C3
commutator, cosocle, hypocenterSU(3,𝔽2)C32
FrattiniC3C3×PSU(3,𝔽2)⋊C3
FittingC3×H(3,𝔽3)SL(2,𝔽3)
prime radicalC3×#272A4
LCSG ▷ SU(3,𝔽2)
UCSC1 ◁ C32

93 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 243

Conjugacy classes & character table

72 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1944, 3444);