Finite Group Databasebeta

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C11×C13⋊C3×C53 #36384392

order22737
automorphism?
homologyAbelianization (H1) = C3×C11×C53 · Schur multiplier (H2) = C1

Aliases

direct productC11×C13⋊C3×C53
unambiguous semidirect productC13⋊(C3×C11×C53)
unambiguous semidirect product(C11×C13)⋊(C3×C53)
unambiguous semidirect product(C13×C53)⋊(C3×C11)
unambiguous semidirect product(C11×C13×C53)⋊C3

Splittings

Fitting, socle, HallC11×C13×C53 ⋊ C3
derived, SylowC13 ⋊ C3×C11×C53
HallC13×C53 ⋊ C3×C11
HallC11×C13 ⋊ C3×C53

Subgroups

subgroupG/H
center, hypercenterC11×C53C13⋊C3
commutator, cosocle, hypocenterC13C3×C11×C53
FrattiniC1G
Fitting, socleC11×C13×C53C3
LCSG ▷ C13
UCSC1 ◁ C11×C53

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7579

Conjugacy classes & character table

4081 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22737, 3);