Finite Group Databasebeta

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C3×C13×C17×C11⋊C5 #49140708

order36465
automorphism?
homologyAbelianization (H1) = C3×C5×C13×C17 · Schur multiplier (H2) = C1

Aliases

direct productC3×C13×C17×C11⋊C5
unambiguous semidirect productC11⋊(C3×C5×C13×C17)
unambiguous semidirect product(C3×C11)⋊(C5×C13×C17)
unambiguous semidirect product(C11×C17)⋊(C3×C5×C13)
unambiguous semidirect product(C3×C11×C13)⋊(C5×C17)
unambiguous semidirect product(C3×C11×C17)⋊(C5×C13)
unambiguous semidirect product(C3×C11×C13×C17)⋊C5

Splittings

Fitting, socle, HallC3×C11×C13×C17 ⋊ C5
derived, SylowC11 ⋊ C3×C5×C13×C17
HallC11×C13×C17 ⋊ C3×C5
HallC3×C11×C17 ⋊ C5×C13
HallC3×C11×C13 ⋊ C5×C17
HallC11×C17 ⋊ C3×C5×C13
HallC11×C13 ⋊ C3×C5×C17
HallC3×C11 ⋊ C5×C13×C17

Subgroups

subgroupG/H
center, hypercenterC3×C13×C17C11⋊C5
commutator, cosocle, hypocenterC11C3×C5×C13×C17
FrattiniC1G
Fitting, socleC3×C11×C13×C17C5
LCSG ▷ C11
UCSC1 ◁ C3×C13×C17

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7293

Conjugacy classes & character table

4641 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36465, 2);