Finite Group Databasebeta

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C2×C9×D493 #31801632

order17748
automorphism?
homologyAbelianization (H1) = C22×C9 · Schur multiplier (H2) = C2

Aliases

direct productC2×C9×D493
unambiguous semidirect product(C2×C17)⋊(C9×D29)
unambiguous semidirect product(C2×C29)⋊(C9×D17)

Splittings

FittingC2×C9×C17×C29 ⋊ C2
derived, HallC17×C29 ⋊ C22×C9
HallC9×C17×C29 ⋊ C22
HallC9×C29 ⋊ C2×D17
HallC9×C17 ⋊ C2×D29
SylowC29 ⋊ C2×C9×D17
SylowC17 ⋊ C2×C9×D29

Subgroups

subgroupG/H
center, hypercenterC2×C9D493
commutator, hypocenterC17×C29C22×C9
FrattiniC3C2×C3×D493
FittingC2×C9×C17×C29C2
socleC2×C3×C17×C29C2×C3
prime radicalC2×C3×D493C3
cosocleC3×C17×C29C22×C3
LCSG ▷ C17×C29
UCSC1 ◁ C2×C9

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8874

Conjugacy classes & character table

4464 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17748, 34);