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C11×C29⋊(D13⋊C3) #38733467

order24882
automorphism?
homologyAbelianization (H1) = C2×C3×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×C29⋊(D13⋊C3)
unambiguous semidirect productC29⋊(C11×D13⋊C3)
unambiguous semidirect product(C13⋊C3)⋊(C11×D29)
unambiguous semidirect productD377⋊(C3×C11)
unambiguous semidirect product(C11×D377)⋊C3

Splittings

Fitting, socle, HallC11×C13×C29 ⋊ C2×C3
derived, HallC13×C29 ⋊ C2×C3×C11
HallC11×C29×C13⋊C3 ⋊ C2
HallC11×D377 ⋊ C3
HallC29×C13⋊C3 ⋊ C2×C11
HallD377 ⋊ C3×C11
HallC11×C13⋊C3 ⋊ D29
HallC11×C29 ⋊ D13⋊C3
HallC11×C13 ⋊ C3×D29
HallC13⋊C3 ⋊ C11×D29
SylowC29 ⋊ C11×D13⋊C3
SylowC13 ⋊ C3×C11×D29

Subgroups

subgroupG/H
center, hypercenterC11C29⋊(D13⋊C3)
commutator, cosocle, hypocenterC13×C29C2×C3×C11
FrattiniC1G
Fitting, socleC11×C13×C29C2×C3
LCSG ▷ C13×C29
UCSC1 ◁ C11

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4147

Conjugacy classes & character table

1166 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24882, 20);