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C3×SL(2,𝔽3)×H(3,𝔽3) #14518862

order1944
automorphism?
homologyAbelianization (H1) = C34 · Schur multiplier (H2) = C37

Aliases

direct productC3×SL(2,𝔽3)×H(3,𝔽3)

Splittings

FittingC3×Q8×H(3,𝔽3) ⋊ C3
SylowQ8 ⋊ C32×H(3,𝔽3)

Subgroups

subgroupG/H
center, socleC2×C32C32×A4
commutator, cosocleC3×Q8C34
FrattiniC2×C3C33×A4
FittingC3×Q8×H(3,𝔽3)C3
hypercenterC2×C3×H(3,𝔽3)A4
hypocenterQ8C32×H(3,𝔽3)
LCSG ▷ C3×Q8 ▷ Q8
UCSC1 ◁ C2×C32 ◁ C2×C3×H(3,𝔽3)

1406 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 216

Conjugacy classes & character table

231 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1944, 3256);