Finite Group Databasebeta

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C2×#66887⋊C5 #72248915

order3520
automorphism?
homologyAbelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C23

Aliases

direct productC2×#66887⋊C5

Splittings

FittingC2×C11×M16 ⋊ C2×C5
HallC2×#66887 ⋊ C5
HallC11⋊C5 ⋊ C2×#100
SylowC11 ⋊ C2×C5×#100

Subgroups

subgroupG/H
centerC22((C2×D11)⋊C4)⋊C5
commutatorC22×C11C22×C4×C5
FrattiniC2×C4C22×AGL(1,𝔽11)
FittingC2×C11×M16C2×C5
socleC22×C11C5×C22⋊C4
prime radicalC22×C4⋊AGL(1,𝔽11)C2
cosocleC2×C4×C11C23×C5
hypercenterC2×M16AGL(1,𝔽11)
hypocenterC11C2×C5×#100
LCSG ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

372 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 372 conjugacy classes of subgroups — too many to draw. Only its 104 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) = 176

Conjugacy classes & character table

130 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×#100×AGL(1,𝔽11), C2×#72222328, C2×#72222331
maximal normal subgroup ofC2×#100×AGL(1,𝔽11), C2×#72222328, C2×#72222331

GAP

Past the SmallGroups library coverage — no SmallGroups id.