Finite Group Databasebeta

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C11×C37×D13⋊C3 #44540813

order31746
automorphism?
homologyAbelianization (H1) = C2×C3×C11×C37 · Schur multiplier (H2) = C1

Aliases

direct productC11×C37×D13⋊C3
unambiguous semidirect productD13⋊(C3×C11×C37)
unambiguous semidirect product(C13⋊C3)⋊(C2×C11×C37)
unambiguous semidirect product(C11×D13)⋊(C3×C37)

Splittings

Fitting, socle, HallC11×C13×C37 ⋊ C2×C3
derived, SylowC13 ⋊ C2×C3×C11×C37
HallC11×C37×C13⋊C3 ⋊ C2
HallC11×D13×C37 ⋊ C3
HallC37×C13⋊C3 ⋊ C2×C11
HallD13×C37 ⋊ C3×C11
HallC13×C37 ⋊ C2×C3×C11
HallC11×C13⋊C3 ⋊ C2×C37
HallC11×D13 ⋊ C3×C37
HallC11×C13 ⋊ C2×C3×C37
HallC13⋊C3 ⋊ C2×C11×C37
HallD13 ⋊ C3×C11×C37

Subgroups

subgroupG/H
center, hypercenterC11×C37D13⋊C3
commutator, cosocle, hypocenterC13C2×C3×C11×C37
FrattiniC1G
Fitting, socleC11×C13×C37C2×C3
LCSG ▷ C13
UCSC1 ◁ C11×C37

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5291

Conjugacy classes & character table

3256 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31746, 26);