Finite Group Databasebeta

← Prev (#31822062) Next (#31822064) →

C2×C32×D71⋊C7 #31822063

order17892
automorphism?
homologyAbelianization (H1) = C22×C32×C7 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C32×D71⋊C7
unambiguous semidirect productD71⋊(C2×C32×C7)
unambiguous semidirect product(C2×D71)⋊(C32×C7)
unambiguous semidirect product(C71⋊C7)⋊(C22×C32)
unambiguous semidirect product(C2×C3×D71)⋊(C3×C7)
unambiguous semidirect product(C2×C71⋊C7)⋊(C2×C32)
unambiguous semidirect product(C2×C32×D71)⋊C7

Splittings

Fitting, socleC2×C32×C71 ⋊ C2×C7
derived, SylowC71 ⋊ C22×C32×C7
HallC32×C71⋊C7 ⋊ C22
HallC2×C32×D71 ⋊ C7
HallC32×C71 ⋊ C22×C7
HallC71⋊C7 ⋊ C22×C32
HallC2×D71 ⋊ C32×C7

Subgroups

subgroupG/H
center, hypercenterC2×C32D71⋊C7
commutator, cosocle, hypocenterC71C22×C32×C7
FrattiniC1G
Fitting, socleC2×C32×C71C2×C7
LCSG ▷ C71
UCSC1 ◁ C2×C32

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1278

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17892, 80);