Finite Group Databasebeta

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C11×C41×D13⋊C3 #47976017

order35178
automorphism?
homologyAbelianization (H1) = C2×C3×C11×C41 · Schur multiplier (H2) = C1

Aliases

direct productC11×C41×D13⋊C3
unambiguous semidirect productD13⋊(C3×C11×C41)
unambiguous semidirect product(C13⋊C3)⋊(C2×C11×C41)
unambiguous semidirect product(C11×D13)⋊(C3×C41)
unambiguous semidirect product(D13×C41)⋊(C3×C11)
unambiguous semidirect product(C11×D13×C41)⋊C3

Splittings

Fitting, socle, HallC11×C13×C41 ⋊ C2×C3
derived, SylowC13 ⋊ C2×C3×C11×C41
HallC11×C13⋊C3×C41 ⋊ C2
HallC11×D13×C41 ⋊ C3
HallC13⋊C3×C41 ⋊ C2×C11
HallD13×C41 ⋊ C3×C11
HallC13×C41 ⋊ C2×C3×C11
HallC11×C13⋊C3 ⋊ C2×C41
HallC11×D13 ⋊ C3×C41
HallC11×C13 ⋊ C2×C3×C41
HallC13⋊C3 ⋊ C2×C11×C41
HallD13 ⋊ C3×C11×C41

Subgroups

subgroupG/H
center, hypercenterC11×C41D13⋊C3
commutator, cosocle, hypocenterC13C2×C3×C11×C41
FrattiniC1G
Fitting, socleC11×C13×C41C2×C3
LCSG ▷ C13
UCSC1 ◁ C11×C41

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5863

Conjugacy classes & character table

3608 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35178, 19);