Finite Group Databasebeta

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3−1+2×C23⋊C11 #72275857

order6831
automorphism?
homologyAbelianization (H1) = C32×C11 · Schur multiplier (H2) = C1

Aliases

direct product3−1+2×C23⋊C11

Splittings

Fitting, HallC23×3−1+2 ⋊ C11
SylowC23 ⋊ C11×3−1+2

Subgroups

subgroupG/H
center, FrattiniC3C32×C23⋊C11
commutator, socle, cosocleC3×C23C32×C11
FittingC23×3−1+2C11
prime radicalC32×C23⋊C11C3
hypercenter3−1+2C23⋊C11
hypocenterC23C11×3−1+2
LCSG ▷ C3×C23 ▷ C23
UCSC1 ◁ C3 ◁ 3−1+2

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 207

Conjugacy classes & character table

143 conjugacy classes — view the full character table.

Relationships

maximal subgroup of3−1+2×AGL(1,𝔽23), AGL(1,ℤ/9)×C23⋊C11, #72275867
maximal normal subgroup of3−1+2×AGL(1,𝔽23), AGL(1,ℤ/9)×C23⋊C11, #72275867

GAP

Past the SmallGroups library coverage — no SmallGroups id.