Finite Group Databasebeta

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C3×C11×C17×C13⋊C3 #36346283

order21879
automorphism?
homologyAbelianization (H1) = C32×C11×C17 · Schur multiplier (H2) = C3

Aliases

direct productC3×C11×C17×C13⋊C3
unambiguous semidirect productC13⋊(C32×C11×C17)
unambiguous semidirect product(C3×C13)⋊(C3×C11×C17)
unambiguous semidirect product(C11×C13)⋊(C32×C17)
unambiguous semidirect product(C13×C17)⋊(C32×C11)
unambiguous semidirect product(C3×C11×C13)⋊(C3×C17)
unambiguous semidirect product(C3×C13×C17)⋊(C3×C11)
unambiguous semidirect product(C11×C13×C17)⋊C32
unambiguous semidirect product(C3×C11×C13×C17)⋊C3

Splittings

Fitting, socleC3×C11×C13×C17 ⋊ C3
derived, SylowC13 ⋊ C32×C11×C17
HallC11×C13×C17 ⋊ C32
HallC13×C17 ⋊ C32×C11
HallC11×C13 ⋊ C32×C17

Subgroups

subgroupG/H
center, hypercenterC3×C11×C17C13⋊C3
commutator, cosocle, hypocenterC13C32×C11×C17
FrattiniC1G
Fitting, socleC3×C11×C13×C17C3
LCSG ▷ C13
UCSC1 ◁ C3×C11×C17

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7293

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, 4);