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C13×D21⋊D11 #26046571

order12012
automorphism?
homologyAbelianization (H1) = C22×C13 · Schur multiplier (H2) = C2

Aliases

direct productC13×D21⋊D11
unambiguous semidirect productD21⋊(C13×D11)
unambiguous semidirect productD33⋊(C13×D7)
unambiguous semidirect productD77⋊(D3×C13)

Splittings

Fitting, socle, HallC3×C7×C11×C13 ⋊ C22
derived, HallC3×C7×C11 ⋊ C22×C13
HallC7×C11×C13 ⋊ C2×D3
HallC3×C11×C13 ⋊ C2×D7
HallC3×C7×C13 ⋊ C2×D11
HallC11×C13 ⋊ D3×D7
HallC7×C13 ⋊ D3×D11
HallC7×C11 ⋊ C2×D3×C13
HallC3×C13 ⋊ D7×D11
HallC3×C11 ⋊ C2×C13×D7
HallC3×C7 ⋊ C2×C13×D11
SylowC11 ⋊ D3×C13×D7
SylowC7 ⋊ D3×C13×D11
SylowC3 ⋊ C13×D7×D11

Subgroups

subgroupG/H
center, hypercenterC13D21⋊D11
commutator, cosocle, hypocenterC3×C7×C11C22×C13
FrattiniC1G
Fitting, socleC3×C7×C11×C13C22
LCSG ▷ C3×C7×C11
UCSC1 ◁ C13

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

975 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC13×D63⋊D11, C13×D33⋊AGL(1,𝔽7), D33⋊#10587720, …
maximal normal subgroup ofC13×D33⋊AGL(1,𝔽7), D33⋊#10587720, D33⋊#10587721, …
maximal quotient ofC13×D63⋊D11, C3×C13×D21⋊D11, C13×D33⋊D21, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12012, 161);