Finite Group Databasebeta

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C17×C22⋊C9×C49 #44472391

order29988
automorphism?
homologyAbelianization (H1) = C9×C17×C49 · Schur multiplier (H2) = C2

Aliases

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

Splittings

derived, SylowC22 ⋊ C9×C17×C49
HallC22×C17×C49 ⋊ C9
HallC22×C49 ⋊ C9×C17
HallC22×C17 ⋊ C9×C49

Subgroups

subgroupG/H
center, hypercenterC3×C17×C49A4
commutator, hypocenterC22C9×C17×C49
FrattiniC3×C7C7×A4×C17
FittingC22×C3×C17×C49C3
socle, prime radicalC22×C3×C7×C17C3×C7
cosocleC22×C3×C7C3×C7×C17
LCSG ▷ C22
UCSC1 ◁ C3×C17×C49

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14994

Conjugacy classes & character table

9996 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29988, 32);