Finite Group Databasebeta

← Prev (#45656788) Next (#45656790) →

D3×C11×D247 #45656789

order32604
automorphism?
homologyAbelianization (H1) = C22×C11 · Schur multiplier (H2) = C2

Aliases

direct productD3×C11×D247
unambiguous semidirect product(D3×C13)⋊(C11×D19)
unambiguous semidirect product(D3×C19)⋊(C11×D13)

Splittings

Fitting, socle, HallC3×C11×C13×C19 ⋊ C22
derived, HallC3×C13×C19 ⋊ C22×C11
HallC11×C13×C19 ⋊ C2×D3
HallC3×C11×C19 ⋊ C2×D13
HallC3×C11×C13 ⋊ C2×D19
HallC13×C19 ⋊ C2×D3×C11
HallC11×C19 ⋊ D3×D13
HallC11×C13 ⋊ D3×D19
HallC3×C19 ⋊ C2×C11×D13
HallC3×C13 ⋊ C2×C11×D19
HallC3×C11 ⋊ C2×D247
SylowC19 ⋊ D3×C11×D13
SylowC13 ⋊ D3×C11×D19
SylowC3 ⋊ C2×C11×D247

Subgroups

subgroupG/H
center, hypercenterC11D3×D247
commutator, cosocle, hypocenterC3×C13×C19C22×C11
FrattiniC1G
Fitting, socleC3×C11×C13×C19C22
LCSG ▷ C3×C13×C19
UCSC1 ◁ C11

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8151

Conjugacy classes & character table

4125 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32604, 139);