Finite Group Databasebeta

← Prev (#36347177) Next (#36347179) →

C2×D47×C13⋊C9 #36347178

order21996
automorphism?
homologyAbelianization (H1) = C22×C9 · Schur multiplier (H2) = C2

Aliases

direct productC2×D47×C13⋊C9
unambiguous semidirect productC47⋊(C22×C13⋊C9)
unambiguous semidirect product(C2×C47)⋊(C2×C13⋊C9)
unambiguous semidirect product(C2×C13×D47)⋊C9

Splittings

derived, HallC13×C47 ⋊ C22×C9
HallC47×C13⋊C9 ⋊ C22
HallC2×C13×D47 ⋊ C9
SylowC47 ⋊ C22×C13⋊C9
SylowC13 ⋊ C2×C9×D47

Subgroups

subgroupG/H
center, hypercenterC2×C3C13⋊C3×D47
commutator, hypocenterC13×C47C22×C9
FrattiniC3C2×C13⋊C3×D47
Fitting, socleC2×C3×C13×C47C2×C3
prime radicalC2×C3×C13×D47C3
cosocleC3×C13×C47C22×C3
LCSG ▷ C13×C47
UCSC1 ◁ C2×C3

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10998

Conjugacy classes & character table

1050 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21996, 19);