Finite Group Databasebeta

← Prev (#45659030) Next (#45659032) →

C11×C3⋊(D71⋊C7) #45659031

order32802
automorphism?
homologyAbelianization (H1) = C2×C7×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×C3⋊(D71⋊C7)
unambiguous semidirect productC3⋊(C11×D71⋊C7)
unambiguous semidirect productD213⋊(C7×C11)
unambiguous semidirect product(C71⋊C7)⋊(D3×C11)
unambiguous semidirect product(C11×D213)⋊C7

Splittings

Fitting, socle, HallC3×C11×C71 ⋊ C2×C7
derived, HallC3×C71 ⋊ C2×C7×C11
HallC3×C11×C71⋊C7 ⋊ C2
HallC11×C71⋊C7 ⋊ D3
HallC11×D213 ⋊ C7
HallC3×C71⋊C7 ⋊ C2×C11
HallC11×C71 ⋊ D3×C7
HallC71⋊C7 ⋊ D3×C11
HallD213 ⋊ C7×C11
SylowC71 ⋊ D3×C7×C11
HallC3×C11 ⋊ D71⋊C7
SylowC3 ⋊ C11×D71⋊C7

Subgroups

subgroupG/H
center, hypercenterC11C3⋊(D71⋊C7)
commutator, cosocle, hypocenterC3×C71C2×C7×C11
FrattiniC1G
Fitting, socleC3×C11×C71C2×C7
LCSG ▷ C3×C71
UCSC1 ◁ C11

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2343

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32802, 23);