Finite Group Databasebeta

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C2×#10588922⋊C3 #72244687

order3456
automorphism?
homologyAbelianization (H1) = C24×C3 · Schur multiplier (H2) = C26

Aliases

direct productC2×#10588922⋊C3

Splittings

FittingC2×3−1+2×H(5,𝔽2) ⋊ C2
Sylow3−1+2 ⋊ C2×#453

Subgroups

subgroupG/H
centerC22#11721704
commutator, cosocleC2×C4×C9C24×C3
FrattiniC2×C3×C4C23×C3×D3
FittingC2×3−1+2×H(5,𝔽2)C2
socleC22×C3C3×#953
hypercenterC2×H(5,𝔽2)AGL(1,ℤ/9)
hypocenterC9C2×C3×#453
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×H(5,𝔽2)

2981 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 144

Conjugacy classes & character table

232 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×AGL(1,ℤ/9)×#453
maximal normal subgroup ofC2×AGL(1,ℤ/9)×#453

GAP

Past the SmallGroups library coverage — no SmallGroups id.