Finite Group Databasebeta

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C11×(C37⋊C3)⋊D13 #44540816

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

Aliases

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

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC11(C37⋊C3)⋊D13
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

1122 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31746, 29);