Finite Group Databasebeta

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C2×S4×AGL(1,ℤ/9) #72220120

order2592
automorphism?
homologyAbelianization (H1) = C23×C3 · Schur multiplier (H2) = C24

Aliases

direct productC2×S4×AGL(1,ℤ/9)

Splittings

FittingC23×3−1+2 ⋊ C2×D3
derivedC9×A4 ⋊ C23×C3

Subgroups

subgroupG/H
center, hypercenterC2S4×AGL(1,ℤ/9)
commutator, cosocle, hypocenterC9×A4C23×C3
FrattiniC3C2×C3×D3×S4
FittingC23×3−1+2C2×D3
socleC23×C3C3×D32
LCSG ▷ C9×A4
UCSC1 ◁ C2

897 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 897 conjugacy classes of subgroups — too many to draw. Only its 79 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 ofAGL(1,ℤ/9)×#5935, AGL(1,ℤ/9)×#5934, D5×S4×AGL(1,ℤ/9), …
maximal normal subgroup ofC4×S4×AGL(1,ℤ/9)
maximal quotient ofD5×S4×AGL(1,ℤ/9), C4×S4×AGL(1,ℤ/9)
automorphism group ofQ8×D9, #3701, C22×C3×D9

GAP

Past the SmallGroups library coverage — no SmallGroups id.