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C2×C3×C22⋊AGL(1,𝔽11) #72216764

order2640
isoclinismisoclinic class of (C11⋊C5)⋊Q8
automorphism?
homologyAbelianization (H1) = C23×C3×C5 · Schur multiplier (H2) = C23

Aliases

direct productC2×C3×C22⋊AGL(1,𝔽11)

Splittings

FittingC23×C3×C11 ⋊ C2×C5
HallC2×C3×C22⋊D11 ⋊ C5
HallC2×C22⋊D11 ⋊ C3×C5
HallC3×C11⋊C5 ⋊ C2×D4
HallC11⋊C5 ⋊ C2×C3×D4
HallC3×C11 ⋊ C2×C5×D4
SylowC11 ⋊ C2×C3×C5×D4

Subgroups

subgroupG/H
centerC22×C3C2×AGL(1,𝔽11)
commutator, cosocleC2×C11C23×C3×C5
FrattiniC2C22×C3×AGL(1,𝔽11)
FittingC23×C3×C11C2×C5
socleC22×C3×C11C22×C5
hypercenterC23×C3AGL(1,𝔽11)
hypocenterC11C2×C3×C5×D4
LCSG ▷ C2×C11 ▷ C11
UCSC1 ◁ C22×C3 ◁ C23×C3

216 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 92 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

174 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C3×D4×AGL(1,𝔽11), C2×D3×C22⋊AGL(1,𝔽11), C2×#72216761, …
maximal normal subgroup ofC2×C3×D4×AGL(1,𝔽11), C2×D3×C22⋊AGL(1,𝔽11), C2×#72216761, …
maximal quotient ofC3×#66985⋊C5, C3×#67002⋊C5, C3×#67006⋊C5, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.