Finite Group Databasebeta

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C13×D1353 #47976013

order35178
automorphism?
homologyAbelianization (H1) = C2×C13 · Schur multiplier (H2) = C1

Aliases

direct productC13×D1353
unambiguous semidirect productC3⋊(C13×D451)
unambiguous semidirect productC11⋊(C13×D123)
unambiguous semidirect productC41⋊(C13×D33)

Splittings

Fitting, socle, HallC3×C11×C13×C41 ⋊ C2
derived, HallC3×C11×C41 ⋊ C2×C13
HallC11×C13×C41 ⋊ D3
HallC3×C13×C41 ⋊ D11
HallC13×C41 ⋊ D33
HallC11×C41 ⋊ D3×C13
HallC3×C11×C13 ⋊ D41
HallC11×C13 ⋊ D123
HallC3×C41 ⋊ C13×D11
SylowC41 ⋊ C13×D33
HallC3×C13 ⋊ D451
HallC3×C11 ⋊ C13×D41
SylowC11 ⋊ C13×D123
SylowC3 ⋊ C13×D451

Subgroups

subgroupG/H
center, hypercenterC13D1353
commutator, cosocle, hypocenterC3×C11×C41C2×C13
FrattiniC1G
Fitting, socleC3×C11×C13×C41C2
LCSG ▷ C3×C11×C41
UCSC1 ◁ C13

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17589

Conjugacy classes & character table

8814 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35178, 15);