Finite Group Databasebeta

← Prev (#72222350) Next (#72222352) →

C2×AGL(1,𝔽5)×AGL(1,ℤ/9) #72222351

order2160
automorphism?
homologyAbelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23

Aliases

direct productC2×AGL(1,𝔽5)×AGL(1,ℤ/9)

Splittings

FittingC2×C5×3−1+2 ⋊ C2×C4
derivedC5×C9 ⋊ C22×C3×C4
HallC5×3−1+2 ⋊ C22×C4
Sylow3−1+2 ⋊ C22×AGL(1,𝔽5)
SylowC5 ⋊ C2×C4×AGL(1,ℤ/9)

Subgroups

subgroupG/H
center, hypercenterC2AGL(1,𝔽5)×AGL(1,ℤ/9)
commutator, hypocenterC5×C9C22×C3×C4
FrattiniC3C2×C3×D3×AGL(1,𝔽5)
FittingC2×C5×3−1+2C2×C4
socleC2×C3×C5C3×C4×D3
prime radicalC2×D5×AGL(1,ℤ/9)C2
cosocleC9×D5C23×C3
LCSG ▷ C5×C9
UCSC1 ◁ C2

340 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 340 conjugacy classes of subgroups — too many to draw. Only its 94 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)×D5⋊AGL(1,𝔽5), D3×AGL(1,𝔽5)×AGL(1,ℤ/9), C2×AGL(1,ℤ/9)×#1043, …
maximal normal subgroup ofC22×AGL(1,𝔽5)×AGL(1,ℤ/9), C4×AGL(1,𝔽5)×AGL(1,ℤ/9), AGL(1,𝔽5)×C4⋊AGL(1,ℤ/9), …
maximal quotient ofAGL(1,ℤ/9)×D5⋊AGL(1,𝔽5), D3×AGL(1,𝔽5)×AGL(1,ℤ/9), C2×AGL(1,ℤ/9)×#1043, …
automorphism group ofDic45, C2×D45
holomorph ofC2×C5×C9

GAP

Past the SmallGroups library coverage — no SmallGroups id.