Finite Group Databasebeta

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C13×D9×D49 #37524112

order22932
automorphism?
homologyAbelianization (H1) = C22×C13 · Schur multiplier (H2) = C2

Aliases

direct productC13×D9×D49
unambiguous semidirect product(D9×C49)⋊(C2×C13)
unambiguous semidirect product(C9×D49)⋊(C2×C13)
unambiguous semidirect productD441⋊(C2×C13)

Splittings

Fitting, HallC9×C13×C49 ⋊ C22
derived, HallC9×C49 ⋊ C22×C13
HallC13×C49 ⋊ C2×D9
HallC9×C13 ⋊ C2×D49
SylowC49 ⋊ C2×C13×D9
SylowC9 ⋊ C2×C13×D49

Subgroups

subgroupG/H
center, hypercenterC13D9×D49
commutator, cosocle, hypocenterC9×C49C22×C13
FrattiniC3×C7D3×C13×D7
FittingC9×C13×C49C22
socleC3×C7×C13D3×D7
LCSG ▷ C9×C49
UCSC1 ◁ C13

90 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5733

Conjugacy classes & character table

2028 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22932, 57);