Finite Group Databasebeta

← Prev (#49114837) Next (#49114839) →

C2×C3×D11×#63270 #49114838

order36036
automorphism?
homologyAbelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C3×D11×#63270
unambiguous semidirect productC11⋊(C22×C3×#63270)
unambiguous semidirect product(C2×C11)⋊(C2×C3×#63270)

Splittings

Fitting, socleC2×C3×C7×C11×C13 ⋊ C2×C3
derived, HallC7×C11×C13 ⋊ C22×C32
HallC3×C11×#63270 ⋊ C22
HallC2×C7×C13×D11 ⋊ C32
HallC2×C13×D11 ⋊ C3×ΓL(1,𝔽8)
HallC2×C7×D11 ⋊ C3×C13⋊C3
HallC11×C13 ⋊ C22×C3×ΓL(1,𝔽8)
HallC7×C13 ⋊ C2×C32×D11
HallC7×C11 ⋊ C22×C3×C13⋊C3
SylowC13 ⋊ C2×C3×ΓL(1,𝔽8)×D11
SylowC11 ⋊ C22×C3×#63270
SylowC7 ⋊ C2×C3×D11×C13⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C3D11×#63270
commutator, cosocle, hypocenterC7×C11×C13C22×C32
FrattiniC1G
Fitting, socleC2×C3×C7×C11×C13C2×C3
LCSG ▷ C7×C11×C13
UCSC1 ◁ C2×C3

240 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 84 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) = 6006

Conjugacy classes & character table

1386 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36036, 506);