Finite Group Databasebeta

C47×C22⋊(C13⋊C9) #36347190

order21996
automorphism?
homologyAbelianization (H1) = C9×C47 · Schur multiplier (H2) = C2

Aliases

direct productC47×C22⋊(C13⋊C9)
unambiguous semidirect productC22⋊(C47×C13⋊C9)
unambiguous semidirect productC13⋊(C22⋊C9×C47)
unambiguous semidirect product(C22×C47)⋊(C13⋊C9)
unambiguous semidirect product(C13×C47)⋊(C22⋊C9)

Splittings

derived, HallC22×C13 ⋊ C9×C47
HallC22×C13×C47 ⋊ C9
HallC13×C47 ⋊ C22⋊C9
HallC22×C47 ⋊ C13⋊C9
SylowC13 ⋊ C22⋊C9×C47
SylowC22 ⋊ C47×C13⋊C9

Subgroups

subgroupG/H
center, hypercenterC3×C47C22⋊(C13⋊C3)
commutator, hypocenterC22×C13C9×C47
FrattiniC3C47×C22⋊(C13⋊C3)
Fitting, socle, prime radicalC22×C3×C13×C47C3
cosocleC22×C3×C13C3×C47
LCSG ▷ C22×C13
UCSC1 ◁ C3×C47

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10998

Conjugacy classes & character table

2820 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21996, 31);