Finite Group Databasebeta

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D3×C7×C11×D13 #26046544

order12012
automorphism?
homologyAbelianization (H1) = C22×C7×C11 · Schur multiplier (H2) = C2

Aliases

direct productD3×C7×C11×D13
unambiguous semidirect product(D3×C13)⋊(C2×C7×C11)
unambiguous semidirect product(C3×D13)⋊(C2×C7×C11)
unambiguous semidirect productD39⋊(C2×C7×C11)

Splittings

Fitting, socle, HallC3×C7×C11×C13 ⋊ C22
derived, HallC3×C13 ⋊ C22×C7×C11
HallC7×C11×C13 ⋊ C2×D3
HallC3×C11×C13 ⋊ C22×C7
HallC3×C7×C13 ⋊ C22×C11
HallC3×C7×C11 ⋊ C2×D13
HallC11×C13 ⋊ C2×D3×C7
HallC7×C13 ⋊ C2×D3×C11
HallC3×C11 ⋊ C2×C7×D13
HallC3×C7 ⋊ C2×C11×D13
SylowC13 ⋊ C2×D3×C7×C11
SylowC3 ⋊ C2×C7×C11×D13

Subgroups

subgroupG/H
center, hypercenterC7×C11D3×D13
commutator, cosocle, hypocenterC3×C13C22×C7×C11
FrattiniC1G
Fitting, socleC3×C7×C11×C13C22
LCSG ▷ C3×C13
UCSC1 ◁ C7×C11

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1848 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC7×C11×D9×D13, D3×C7×C11×D13⋊C3, D3×C11×#10587716, …
maximal normal subgroup ofD3×C7×C11×D13⋊C3, D3×C11×#10587716, D3×C11×#10587717, …
maximal quotient ofC7×C11×D9×D13, C3×D3×C7×C11×D13, D3×C7×C11×D39, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12012, 134);