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3−1+2×AGL(1,ℤ/9) #13091520

order1458
automorphism?
homologyAbelianization (H1) = C2×C33 · Schur multiplier (H2) = C32

Aliases

direct product3−1+2×AGL(1,ℤ/9)

Splittings

Fitting, Sylow3−1+22 ⋊ C2

Subgroups

subgroupG/H
centerC3C32×AGL(1,ℤ/9)
commutator, cosocleC3×C9C2×C33
Frattini, socleC32C33×D3
Fitting3−1+22C2
prime radicalC32×AGL(1,ℤ/9)C3
hypercenter3−1+2AGL(1,ℤ/9)
hypocenterC9C2×C3×3−1+2
LCSG ▷ C3×C9 ▷ C9
UCSC1 ◁ C3 ◁ 3−1+2

380 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 103 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 54

Conjugacy classes & character table

110 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,ℤ/9)2, C2×3−1+2×AGL(1,ℤ/9), 3−1+2×C3⋊AGL(1,ℤ/9), …
maximal normal subgroup ofAGL(1,ℤ/9)2, C2×3−1+2×AGL(1,ℤ/9), C3×3−1+2×AGL(1,ℤ/9), …
maximal quotient ofC2×3−1+2×AGL(1,ℤ/9), 3−1+2×3−1+2⋊C4, 3−1+2×C3⋊AGL(1,ℤ/9), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1458, 1594);