Finite Group Databasebeta

← Prev (#72216612) Next (#72216614) →

C22×D4×AGL(1,𝔽11) #72216613

order3520
automorphism?
homologyAbelianization (H1) = C25×C5 · Schur multiplier (H2) = C210

Aliases

direct productC22×D4×AGL(1,𝔽11)

Splittings

FittingC22×D4×C11 ⋊ C2×C5
HallC22×D4×D11 ⋊ C5
HallC11⋊C5 ⋊ C23×D4
SylowC11 ⋊ C23×C5×D4

Subgroups

subgroupG/H
centerC23C22×AGL(1,𝔽11)
commutator, cosocleC2×C11C25×C5
FrattiniC2C24×AGL(1,𝔽11)
FittingC22×D4×C11C2×C5
socleC23×C11C23×C5
hypercenterC22×D4AGL(1,𝔽11)
hypocenterC11C23×C5×D4
LCSG ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×D4

2724 conjugacy classes of subgroups; only the 928 normal subgroups are shown.

normal subgroups only

This group has 2724 conjugacy classes of subgroups — too many to draw. Only its 928 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

220 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×#120×AGL(1,𝔽11), C2×D3×D4×AGL(1,𝔽11), C2×AGL(1,ℤ/8)×AGL(1,𝔽11), …
maximal normal subgroup ofC2×#120×AGL(1,𝔽11), C2×AGL(1,ℤ/8)×AGL(1,𝔽11), C2×H(5,𝔽2)×AGL(1,𝔽11), …
maximal quotient ofC2×#120×AGL(1,𝔽11), C2×D3×D4×AGL(1,𝔽11), C2×AGL(1,ℤ/8)×AGL(1,𝔽11), …
automorphism group ofC3×#4323, C3×#4324, C3×#4325, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.