Finite Group Databasebeta

← Prev (#39911629) Next (#39911631) →

C17×C22⋊(C43⋊C9) #39911630

order26316
automorphism?
homologyAbelianization (H1) = C9×C17 · Schur multiplier (H2) = C2

Aliases

direct productC17×C22⋊(C43⋊C9)
unambiguous semidirect productC22⋊(C17×C43⋊C9)
unambiguous semidirect productC43⋊(C17×C22⋊C9)
unambiguous semidirect product(C22×C17)⋊(C43⋊C9)
unambiguous semidirect product(C17×C43)⋊(C22⋊C9)

Splittings

derived, HallC22×C43 ⋊ C9×C17
HallC22×C17×C43 ⋊ C9
HallC17×C43 ⋊ C22⋊C9
HallC22×C17 ⋊ C43⋊C9
SylowC43 ⋊ C17×C22⋊C9
SylowC22 ⋊ C17×C43⋊C9

Subgroups

subgroupG/H
center, hypercenterC3×C17C22⋊(C43⋊C3)
commutator, hypocenterC22×C43C9×C17
FrattiniC3C17×C22⋊(C43⋊C3)
Fitting, socle, prime radicalC22×C3×C17×C43C3
cosocleC22×C3×C43C3×C17
LCSG ▷ C22×C43
UCSC1 ◁ C3×C17

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 13158

Conjugacy classes & character table

3060 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26316, 31);