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3−1+2×#226 #13048364

order1296
automorphism?
homologyAbelianization (H1) = C2×C32 · Schur multiplier (H2) = C1

Aliases

direct product3−1+2×#226
unambiguous semidirect product(C9×#226)⋊C3

Subgroups

subgroupG/H
center, Frattini, socleC2×C3C32×S4
commutator, cosocleC3×SL(2,𝔽3)C2×C32
FittingQ8×3−1+2D3
prime radicalC32×SL(2,𝔽3)C2×C3
hypercenterC2×3−1+2S4
hypocenterSL(2,𝔽3)C2×3−1+2
LCSG ▷ C3×SL(2,𝔽3) ▷ SL(2,𝔽3)
UCSC1 ◁ C2×C3 ◁ C2×3−1+2

137 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 144

Conjugacy classes & character table

88 conjugacy classes — view the full character table.

Relationships

maximal subgroup of3−1+2×#5933, #72253021
maximal quotient of#72253018

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1296, 2082);