Finite Group Databasebeta

← Prev (#45659009) Next (#45659011) →

C2×C3×C11×C71⋊C7 #45659010

order32802
automorphism?
homologyAbelianization (H1) = C2×C3×C7×C11 · Schur multiplier (H2) = C1

Aliases

direct productC2×C3×C11×C71⋊C7
unambiguous semidirect product(C2×C71)⋊(C3×C7×C11)
unambiguous semidirect product(C2×C3×C71)⋊(C7×C11)
unambiguous semidirect product(C2×C11×C71)⋊(C3×C7)
unambiguous semidirect product(C2×C3×C11×C71)⋊C7

Splittings

Fitting, socle, HallC2×C3×C11×C71 ⋊ C7
derived, SylowC71 ⋊ C2×C3×C7×C11
HallC3×C11×C71 ⋊ C2×C7
HallC2×C11×C71 ⋊ C3×C7
HallC11×C71 ⋊ C2×C3×C7
HallC2×C3×C71 ⋊ C7×C11
HallC3×C71 ⋊ C2×C7×C11
HallC2×C71 ⋊ C3×C7×C11

Subgroups

subgroupG/H
center, hypercenterC2×C3×C11C71⋊C7
commutator, cosocle, hypocenterC71C2×C3×C7×C11
FrattiniC1G
Fitting, socleC2×C3×C11×C71C7
LCSG ▷ C71
UCSC1 ◁ C2×C3×C11

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4686

Conjugacy classes & character table

1122 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32802, 2);