Finite Group Databasebeta

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C17×C22⋊(C49⋊C9) #44472392

order29988
automorphism?
homologyAbelianization (H1) = C9×C17 · Schur multiplier (H2) = C2

Aliases

direct productC17×C22⋊(C49⋊C9)
unambiguous semidirect productC22⋊(C17×C49⋊C9)
unambiguous semidirect productC49⋊(C17×C22⋊C9)
unambiguous semidirect product(C22×C17)⋊(C49⋊C9)
unambiguous semidirect product(C17×C49)⋊(C22⋊C9)

Splittings

derived, HallC22×C49 ⋊ C9×C17
HallC22×C17×C49 ⋊ C9
HallC17×C49 ⋊ C22⋊C9
HallC22×C17 ⋊ C49⋊C9
SylowC49 ⋊ C17×C22⋊C9
SylowC22 ⋊ C17×C49⋊C9

Subgroups

subgroupG/H
center, hypercenterC3×C17C22⋊(C49⋊C3)
commutator, hypocenterC22×C49C9×C17
FrattiniC3×C7C17×C22⋊ΓL(1,𝔽8)
FittingC22×C3×C17×C49C3
socle, prime radicalC22×C3×C7×C17ΓL(1,𝔽8)
cosocleC22×C3×C49C3×C17
LCSG ▷ C22×C49
UCSC1 ◁ C3×C17

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14994

Conjugacy classes & character table

3468 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29988, 33);