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C43×C11⋊(D13⋊C3) #49146334

order36894
automorphism?
homologyAbelianization (H1) = C2×C3×C43 · Schur multiplier (H2) = C1

Aliases

direct productC43×C11⋊(D13⋊C3)
unambiguous semidirect productC11⋊(C43×D13⋊C3)
unambiguous semidirect product(C13⋊C3)⋊(D11×C43)
unambiguous semidirect productD143⋊(C3×C43)

Splittings

Fitting, socle, HallC11×C13×C43 ⋊ C2×C3
derived, HallC11×C13 ⋊ C2×C3×C43
HallC11×C13⋊C3×C43 ⋊ C2
HallC43×D143 ⋊ C3
HallC13⋊C3×C43 ⋊ D11
HallC13×C43 ⋊ C3×D11
HallC11×C43 ⋊ D13⋊C3
HallC11×C13⋊C3 ⋊ C2×C43
HallD143 ⋊ C3×C43
HallC13⋊C3 ⋊ D11×C43
SylowC13 ⋊ C3×D11×C43
SylowC11 ⋊ C43×D13⋊C3

Subgroups

subgroupG/H
center, hypercenterC43C11⋊(D13⋊C3)
commutator, cosocle, hypocenterC11×C13C2×C3×C43
FrattiniC1G
Fitting, socleC11×C13×C43C2×C3
LCSG ▷ C11×C13
UCSC1 ◁ C43

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6149

Conjugacy classes & character table

1849 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36894, 42);