Finite Group Databasebeta

← Prev (#44541816) Next (#44541818) →

C3×C11×D483 #44541817

order31878
automorphism?
homologyAbelianization (H1) = C2×C3×C11 · Schur multiplier (H2) = C1

Aliases

direct productC3×C11×D483
unambiguous semidirect productC3⋊(C3×C11×D161)

Splittings

Fitting, socle, HallC32×C7×C11×C23 ⋊ C2
derivedC3×C7×C23 ⋊ C2×C3×C11
HallC32×C11×C23 ⋊ D7
HallC7×C11×C23 ⋊ C3×D3
HallC32×C7×C23 ⋊ C2×C11
HallC32×C7×C11 ⋊ D23
HallC11×C23 ⋊ C3×D21
HallC32×C23 ⋊ C11×D7
HallC7×C23 ⋊ C3×D3×C11
HallC32×C11 ⋊ D161
HallC7×C11 ⋊ C3×D69
HallC32×C7 ⋊ C11×D23
SylowC23 ⋊ C3×C11×D21
SylowC32 ⋊ C11×D161
SylowC7 ⋊ C3×C11×D69

Subgroups

subgroupG/H
center, hypercenterC3×C11D483
commutator, cosocle, hypocenterC3×C7×C23C2×C3×C11
FrattiniC1G
Fitting, socleC32×C7×C11×C23C2
LCSG ▷ C3×C7×C23
UCSC1 ◁ C3×C11

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10626

Conjugacy classes & character table

8019 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31878, 86);