Finite Group Databasebeta

← Prev (#72216633) Next (#72216635) →

C2×#120×C11⋊C5 #72216634

order3520
automorphism?
homologyAbelianization (H1) = C24×C5 · Schur multiplier (H2) = C27

Aliases

direct productC2×#120×C11⋊C5

Splittings

Fitting, HallC2×C11×#120 ⋊ C5
SylowC11 ⋊ C2×C5×#120

Subgroups

subgroupG/H
centerC23C23×C11⋊C5
commutator, cosocleC22×C11C24×C5
FrattiniC22C24×C11⋊C5
FittingC2×C11×#120C5
socleC23×C11C23×C5
hypercenterC2×#120C11⋊C5
hypocenterC11C2×C5×#120
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#120

1324 conjugacy classes of subgroups; only the 315 normal subgroups are shown.

normal subgroups only

This group has 1324 conjugacy classes of subgroups — too many to draw. Only its 315 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

196 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×#120×AGL(1,𝔽11), D3×#120×C11⋊C5, C22×#120×C11⋊C5, …
maximal normal subgroup ofC2×#120×AGL(1,𝔽11), C22×#120×C11⋊C5, C11⋊C5×#3484, …
maximal quotient ofD3×#120×C11⋊C5, C22×#120×C11⋊C5, C2×C11⋊C5×#453

GAP

Past the SmallGroups library coverage — no SmallGroups id.