Finite Group Databasebeta

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C13×C11⋊(D37⋊C3) #44540824

order31746
automorphism?
homologyAbelianization (H1) = C2×C3×C13 · Schur multiplier (H2) = C1

Aliases

direct productC13×C11⋊(D37⋊C3)
unambiguous semidirect productC11⋊(C13×D37⋊C3)
unambiguous semidirect product(C37⋊C3)⋊(C13×D11)
unambiguous semidirect productD407⋊(C3×C13)

Splittings

Fitting, socle, HallC11×C13×C37 ⋊ C2×C3
derived, HallC11×C37 ⋊ C2×C3×C13
HallC11×C13×C37⋊C3 ⋊ C2
HallC13×D407 ⋊ C3
HallC13×C37⋊C3 ⋊ D11
HallC11×C37⋊C3 ⋊ C2×C13
HallD407 ⋊ C3×C13
HallC13×C37 ⋊ C3×D11
HallC11×C13 ⋊ D37⋊C3
HallC37⋊C3 ⋊ C13×D11
SylowC37 ⋊ C3×C13×D11
SylowC11 ⋊ C13×D37⋊C3

Subgroups

subgroupG/H
center, hypercenterC13C11⋊(D37⋊C3)
commutator, cosocle, hypocenterC11×C37C2×C3×C13
FrattiniC1G
Fitting, socleC11×C13×C37C2×C3
LCSG ▷ C11×C37
UCSC1 ◁ C13

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5291

Conjugacy classes & character table

1131 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31746, 37);