Finite Group Databasebeta

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C2×C11×C13×C37⋊C3 #44540789

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

Aliases

direct productC2×C11×C13×C37⋊C3
unambiguous semidirect product(C2×C37)⋊(C3×C11×C13)
unambiguous semidirect product(C2×C11×C37)⋊(C3×C13)

Splittings

Fitting, socle, HallC2×C11×C13×C37 ⋊ C3
derived, SylowC37 ⋊ C2×C3×C11×C13
HallC11×C13×C37 ⋊ C2×C3
HallC2×C13×C37 ⋊ C3×C11
HallC2×C11×C37 ⋊ C3×C13
HallC13×C37 ⋊ C2×C3×C11
HallC11×C37 ⋊ C2×C3×C13
HallC2×C37 ⋊ C3×C11×C13

Subgroups

subgroupG/H
center, hypercenterC2×C11×C13C37⋊C3
commutator, cosocle, hypocenterC37C2×C3×C11×C13
FrattiniC1G
Fitting, socleC2×C11×C13×C37C3
LCSG ▷ C37
UCSC1 ◁ C2×C11×C13

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10582

Conjugacy classes & character table

4290 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31746, 2);