Finite Group Databasebeta

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C22×#66990⋊C5 #72254516

order7040
automorphism?
homologyAbelianization (H1) = C25×C5 · Schur multiplier (H2) = C211

Aliases

direct productC22×#66990⋊C5

Splittings

FittingC23×D4×C11 ⋊ C2×C5
HallC22×#66990 ⋊ C5
HallC11⋊C5 ⋊ C22×#120
SylowC11 ⋊ C22×C5×#120

Subgroups

subgroupG/H
centerC24C22×AGL(1,𝔽11)
commutator, cosocleC22×C11C25×C5
FrattiniC22C24×AGL(1,𝔽11)
FittingC23×D4×C11C2×C5
socleC24×C11C23×C5
hypercenterC23×D4AGL(1,𝔽11)
hypocenterC11C22×C5×#120
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ C23×D4

9088 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 352

Conjugacy classes & character table

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

GAP

Past the SmallGroups library coverage — no SmallGroups id.