Finite Group Databasebeta

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C11×C17×C13⋊C9 #36346281

order21879
automorphism?
homologyAbelianization (H1) = C9×C11×C17 · Schur multiplier (H2) = C1

Aliases

direct productC11×C17×C13⋊C9
unambiguous semidirect productC13⋊(C9×C11×C17)
unambiguous semidirect product(C11×C13)⋊(C9×C17)
unambiguous semidirect product(C13×C17)⋊(C9×C11)
unambiguous semidirect product(C11×C13×C17)⋊C9

Splittings

derived, SylowC13 ⋊ C9×C11×C17
HallC11×C13×C17 ⋊ C9
HallC13×C17 ⋊ C9×C11
HallC11×C13 ⋊ C9×C17

Subgroups

subgroupG/H
center, hypercenterC3×C11×C17C13⋊C3
commutator, hypocenterC13C9×C11×C17
FrattiniC3C11×C17×C13⋊C3
Fitting, socle, prime radicalC3×C11×C13×C17C3
cosocleC3×C13C3×C11×C17
LCSG ▷ C13
UCSC1 ◁ C3×C11×C17

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 21879

Conjugacy classes & character table

3927 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21879, 2);