Finite Group Databasebeta

← Prev (#44568349) Next (#44568351) →

C5×D11×D49⋊C3 #44568350

order32340
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC5×D11×D49⋊C3
unambiguous semidirect productD49⋊(C3×C5×D11)
unambiguous semidirect product(C5×D11×D49)⋊C3

Splittings

Fitting, HallC5×C11×C49 ⋊ C22×C3
derived, HallC11×C49 ⋊ C22×C3×C5
HallC5×D11×D49 ⋊ C3
HallC5×C11×C49⋊C3 ⋊ C22
HallD11×D49 ⋊ C3×C5
HallC11×C49⋊C3 ⋊ C22×C5
HallC5×C49⋊C3 ⋊ C2×D11
HallC5×C49 ⋊ C2×C3×D11
HallC49⋊C3 ⋊ C2×C5×D11
HallC5×C11 ⋊ C2×D49⋊C3
SylowC49 ⋊ C2×C3×C5×D11
SylowC11 ⋊ C2×C5×D49⋊C3

Subgroups

subgroupG/H
center, hypercenterC5D11×D49⋊C3
commutator, cosocle, hypocenterC11×C49C22×C3×C5
FrattiniC7C5×D11×AGL(1,𝔽7)
FittingC5×C11×C49C22×C3
socleC5×C7×C11C2×AGL(1,𝔽7)
LCSG ▷ C11×C49
UCSC1 ◁ C5

120 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 40 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) = 2695

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 52);