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H(3,𝔽3)×#226 #13048362

order1296
automorphism?
homologyAbelianization (H1) = C2×C32 · Schur multiplier (H2) = C32

Aliases

direct productH(3,𝔽3)×#226
unambiguous semidirect product(C32×#226)⋊C3

Subgroups

subgroupG/H
center, Frattini, socleC2×C3C32×S4
commutator, cosocleC3×SL(2,𝔽3)C2×C32
FittingQ8×H(3,𝔽3)D3
prime radicalSL(2,𝔽3)×H(3,𝔽3)C2
hypercenterC2×H(3,𝔽3)S4
hypocenterSL(2,𝔽3)C2×H(3,𝔽3)
LCSG ▷ C3×SL(2,𝔽3) ▷ SL(2,𝔽3)
UCSC1 ◁ C2×C3 ◁ C2×H(3,𝔽3)

194 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 144

Conjugacy classes & character table

88 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1296, 2080);