Finite Group Databasebeta

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C11×C13⋊C3×D41 #47976016

order35178
automorphism?
homologyAbelianization (H1) = C2×C3×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×C13⋊C3×D41
unambiguous semidirect productC41⋊(C2×C11×C13⋊C3)
unambiguous semidirect product(C13×D41)⋊(C3×C11)
unambiguous semidirect product(C11×C13×D41)⋊C3

Splittings

Fitting, socle, HallC11×C13×C41 ⋊ C2×C3
derived, HallC13×C41 ⋊ C2×C3×C11
HallC11×C13⋊C3×C41 ⋊ C2
HallC11×C13×D41 ⋊ C3
HallC13⋊C3×C41 ⋊ C2×C11
HallC13×D41 ⋊ C3×C11
HallC11×C41 ⋊ C2×C13⋊C3
HallC11×C13 ⋊ C3×D41
SylowC41 ⋊ C2×C11×C13⋊C3
SylowC13 ⋊ C3×C11×D41

Subgroups

subgroupG/H
center, hypercenterC11C13⋊C3×D41
commutator, cosocle, hypocenterC13×C41C2×C3×C11
FrattiniC1G
Fitting, socleC11×C13×C41C2×C3
LCSG ▷ C13×C41
UCSC1 ◁ C11

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5863

Conjugacy classes & character table

1694 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35178, 18);