Finite Group Databasebeta

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AGL(1,ℤ/9)2 #72214411

order2916
automorphism?
homologyAbelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3

Aliases

direct productAGL(1,ℤ/9)2

Splittings

Fitting, Sylow3−1+22 ⋊ C22
derivedC92 ⋊ C22×C32

Subgroups

subgroupG/H
center, hypercenterC1G
commutator, cosocle, hypocenterC92C22×C32
Frattini, socleC32C32×D32
Fitting3−1+22C22
LCSG ▷ C92
UCSC1

490 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 490 conjugacy classes of subgroups — too many to draw. Only its 73 normal subgroups are shown.

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

Full subgroup data →

Conjugacy classes & character table

100 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×AGL(1,ℤ/9)2, AGL(1,ℤ/9)×C3⋊AGL(1,ℤ/9), C3×AGL(1,ℤ/9)2, …
maximal normal subgroup ofC2×AGL(1,ℤ/9)2, C3×AGL(1,ℤ/9)2
maximal quotient ofC2×AGL(1,ℤ/9)2, #72228945, #72228948, …
holomorph ofAGL(1,ℤ/9)

GAP

Past the SmallGroups library coverage — no SmallGroups id.