Finite Group Databasebeta

← Prev (#49114684) Next (#49114686) →

D3×C7×C11⋊(D13⋊C3) #49114685

order36036
automorphism?
homologyAbelianization (H1) = C22×C3×C7 · Schur multiplier (H2) = C2

Aliases

direct productD3×C7×C11⋊(D13⋊C3)
unambiguous semidirect product(D3×C11)⋊(C7×D13⋊C3)
unambiguous semidirect product(D3×C13⋊C3)⋊(C7×D11)
unambiguous semidirect product(D3×D143)⋊(C3×C7)

Splittings

Fitting, socleC3×C7×C11×C13 ⋊ C22×C3
derivedC3×C11×C13 ⋊ C22×C3×C7
HallC3×C7×C11×C13⋊C3 ⋊ C22
HallC3×C11×C13⋊C3 ⋊ C22×C7
HallC7×C11×C13 ⋊ C2×C3×D3
HallC3×C7×C13⋊C3 ⋊ C2×D11
HallC11×C13 ⋊ C2×C3×D3×C7
HallC3×C13⋊C3 ⋊ C2×C7×D11
HallC7×C13 ⋊ C3×D3×D11
HallC7×C11 ⋊ D3×D13⋊C3
SylowC13 ⋊ C3×D3×C7×D11
SylowC11 ⋊ D3×C7×D13⋊C3

Subgroups

subgroupG/H
center, hypercenterC7D3×C11⋊(D13⋊C3)
commutator, cosocle, hypocenterC3×C11×C13C22×C3×C7
FrattiniC1G
Fitting, socleC3×C7×C11×C13C22×C3
LCSG ▷ C3×C11×C13
UCSC1 ◁ C7

176 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 52 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) = 3003

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36036, 353);