Finite Group Databasebeta

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C11×(C13⋊C3)⋊D37 #44540817

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

Aliases

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

Splittings

Fitting, socle, HallC11×C13×C37 ⋊ C2×C3
derived, HallC13×C37 ⋊ C2×C3×C11
HallC11×C37×C13⋊C3 ⋊ C2
HallC11×D481 ⋊ C3
HallC37×C13⋊C3 ⋊ C2×C11
HallD481 ⋊ C3×C11
HallC11×C13⋊C3 ⋊ D37
HallC11×C37 ⋊ D13⋊C3
HallC11×C13 ⋊ C3×D37
HallC13⋊C3 ⋊ C11×D37
SylowC37 ⋊ C11×D13⋊C3
SylowC13 ⋊ C3×C11×D37

Subgroups

subgroupG/H
center, hypercenterC11(C13⋊C3)⋊D37
commutator, cosocle, hypocenterC13×C37C2×C3×C11
FrattiniC1G
Fitting, socleC11×C13×C37C2×C3
LCSG ▷ C13×C37
UCSC1 ◁ C11

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5291

Conjugacy classes & character table

1474 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31746, 30);