Finite Group Databasebeta

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C13×D1221 #44540805

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

Aliases

direct productC13×D1221
unambiguous semidirect productC3⋊(C13×D407)
unambiguous semidirect productC11⋊(C13×D111)
unambiguous semidirect productC37⋊(C13×D33)

Splittings

Fitting, socle, HallC3×C11×C13×C37 ⋊ C2
derived, HallC3×C11×C37 ⋊ C2×C13
HallC11×C13×C37 ⋊ D3
HallC3×C13×C37 ⋊ D11
HallC13×C37 ⋊ D33
HallC3×C11×C13 ⋊ D37
HallC11×C37 ⋊ D3×C13
HallC11×C13 ⋊ D111
HallC3×C37 ⋊ C13×D11
HallC3×C13 ⋊ D407
SylowC37 ⋊ C13×D33
HallC3×C11 ⋊ C13×D37
SylowC11 ⋊ C13×D111
SylowC3 ⋊ C13×D407

Subgroups

subgroupG/H
center, hypercenterC13D1221
commutator, cosocle, hypocenterC3×C11×C37C2×C13
FrattiniC1G
Fitting, socleC3×C11×C13×C37C2
LCSG ▷ C3×C11×C37
UCSC1 ◁ C13

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15873

Conjugacy classes & character table

7956 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31746, 18);