Finite Group Databasebeta

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C17×C13⋊C3×C49 #44570402

order32487
automorphism?
homologyAbelianization (H1) = C3×C17×C49 · Schur multiplier (H2) = C1

Aliases

direct productC17×C13⋊C3×C49
unambiguous semidirect productC13⋊(C3×C17×C49)
unambiguous semidirect product(C13×C17)⋊(C3×C49)

Splittings

Fitting, HallC13×C17×C49 ⋊ C3
derived, SylowC13 ⋊ C3×C17×C49
HallC13×C49 ⋊ C3×C17
HallC13×C17 ⋊ C3×C49

Subgroups

subgroupG/H
center, hypercenterC17×C49C13⋊C3
commutator, hypocenterC13C3×C17×C49
FrattiniC7C7×C17×C13⋊C3
FittingC13×C17×C49C3
socleC7×C13×C17C3×C7
prime radicalC7×C17×C13⋊C3C7
cosocleC7×C13C3×C7×C17
LCSG ▷ C13
UCSC1 ◁ C17×C49

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10829

Conjugacy classes & character table

5831 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32487, 2);