Finite Group Databasebeta

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C2×#66990⋊C5 #72216638

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

Aliases

direct productC2×#66990⋊C5

Splittings

FittingC22×D4×C11 ⋊ C2×C5
HallC2×#66990 ⋊ C5
HallC11⋊C5 ⋊ C2×#120
SylowC11 ⋊ C2×C5×#120

Subgroups

subgroupG/H
centerC23C22×AGL(1,𝔽11)
commutator, cosocleC22×C11C24×C5
FrattiniC22C23×AGL(1,𝔽11)
FittingC22×D4×C11C2×C5
socleC23×C11C23×C5
hypercenterC22×D4AGL(1,𝔽11)
hypocenterC11C2×C5×#120
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×D4

1324 conjugacy classes of subgroups; only the 248 normal subgroups are shown.

normal subgroups only

This group has 1324 conjugacy classes of subgroups — too many to draw. Only its 248 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

160 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×#120×AGL(1,𝔽11), D3×#66990⋊C5, #72248978, …
maximal normal subgroup ofC2×#120×AGL(1,𝔽11), #72248978, C22×#66990⋊C5, …
maximal quotient ofD3×#66990⋊C5, C2×#72222328, C2×#72222335, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.