Finite Group Databasebeta

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C22×C22⋊C4×C11⋊C5 #72248834

order3520
automorphism?
homologyAbelianization (H1) = C23×C4×C5 · Schur multiplier (H2) = C27

Aliases

direct productC22×C22⋊C4×C11⋊C5

Splittings

Fitting, HallC22×C11×C22⋊C4 ⋊ C5
SylowC11 ⋊ C22×C5×C22⋊C4

Subgroups

subgroupG/H
centerC24C22×C11⋊C5
commutatorC2×C11C23×C4×C5
FrattiniC22C24×C11⋊C5
FittingC22×C11×C22⋊C4C5
socleC24×C11C22×C5
prime radicalC25×C11⋊C5C2
cosocleC22×C11C24×C5
hypercenterC22×C22⋊C4C11⋊C5
hypocenterC11C22×C5×C22⋊C4
LCSG ▷ C2×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×C22⋊C4

1348 conjugacy classes of subgroups; only the 507 normal subgroups are shown.

normal subgroups only

This group has 1348 conjugacy classes of subgroups — too many to draw. Only its 507 normal subgroups are shown.

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

Full subgroup data →

Presentation

transitive degreeμt(G) = 352

Conjugacy classes & character table

280 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×#120×C11⋊C5, C22×C22⋊C4×AGL(1,𝔽11), C22×#66935⋊C5
maximal normal subgroup ofC22×#120×C11⋊C5, C22×C22⋊C4×AGL(1,𝔽11), C22×#66935⋊C5

GAP

Past the SmallGroups library coverage — no SmallGroups id.