Finite Group Databasebeta

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C11×C13×D37⋊C3 #44540808

order31746
automorphism?
homologyAbelianization (H1) = C2×C3×C11×C13 · Schur multiplier (H2) = C1

Aliases

direct productC11×C13×D37⋊C3
unambiguous semidirect productD37⋊(C3×C11×C13)
unambiguous semidirect product(C37⋊C3)⋊(C2×C11×C13)
unambiguous semidirect product(C11×D37)⋊(C3×C13)

Splittings

Fitting, socle, HallC11×C13×C37 ⋊ C2×C3
derived, SylowC37 ⋊ C2×C3×C11×C13
HallC11×C13×C37⋊C3 ⋊ C2
HallC11×C13×D37 ⋊ C3
HallC13×C37⋊C3 ⋊ C2×C11
HallC11×C37⋊C3 ⋊ C2×C13
HallC13×D37 ⋊ C3×C11
HallC11×D37 ⋊ C3×C13
HallC13×C37 ⋊ C2×C3×C11
HallC11×C37 ⋊ C2×C3×C13
HallC37⋊C3 ⋊ C2×C11×C13
HallD37 ⋊ C3×C11×C13

Subgroups

subgroupG/H
center, hypercenterC11×C13D37⋊C3
commutator, cosocle, hypocenterC37C2×C3×C11×C13
FrattiniC1G
Fitting, socleC11×C13×C37C2×C3
LCSG ▷ C37
UCSC1 ◁ C11×C13

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5291

Conjugacy classes & character table

1716 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31746, 21);