Finite Group Databasebeta

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C5×C11×C17×C13⋊C3 #49140709

order36465
automorphism?
homologyAbelianization (H1) = C3×C5×C11×C17 · Schur multiplier (H2) = C1

Aliases

direct productC5×C11×C17×C13⋊C3
unambiguous semidirect productC13⋊(C3×C5×C11×C17)
unambiguous semidirect product(C5×C13)⋊(C3×C11×C17)
unambiguous semidirect product(C13×C17)⋊(C3×C5×C11)
unambiguous semidirect product(C5×C11×C13)⋊(C3×C17)
unambiguous semidirect product(C5×C13×C17)⋊(C3×C11)
unambiguous semidirect product(C5×C11×C13×C17)⋊C3

Splittings

Fitting, socle, HallC5×C11×C13×C17 ⋊ C3
derived, SylowC13 ⋊ C3×C5×C11×C17
HallC11×C13×C17 ⋊ C3×C5
HallC5×C13×C17 ⋊ C3×C11
HallC5×C11×C13 ⋊ C3×C17
HallC13×C17 ⋊ C3×C5×C11
HallC11×C13 ⋊ C3×C5×C17
HallC5×C13 ⋊ C3×C11×C17

Subgroups

subgroupG/H
center, hypercenterC5×C11×C17C13⋊C3
commutator, cosocle, hypocenterC13C3×C5×C11×C17
FrattiniC1G
Fitting, socleC5×C11×C13×C17C3
LCSG ▷ C13
UCSC1 ◁ C5×C11×C17

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12155

Conjugacy classes & character table

6545 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36465, 3);