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C29×D429 #38733463

order24882
automorphism?
homologyAbelianization (H1) = C2×C29 · Schur multiplier (H2) = C1

Aliases

direct productC29×D429
unambiguous semidirect productC3⋊(C29×D143)
unambiguous semidirect productC11⋊(C29×D39)
unambiguous semidirect productC13⋊(C29×D33)

Splittings

Fitting, socle, HallC3×C11×C13×C29 ⋊ C2
derived, HallC3×C11×C13 ⋊ C2×C29
HallC11×C13×C29 ⋊ D3
HallC3×C13×C29 ⋊ D11
HallC3×C11×C29 ⋊ D13
HallC13×C29 ⋊ D33
HallC11×C29 ⋊ D39
HallC11×C13 ⋊ D3×C29
HallC3×C29 ⋊ D143
HallC3×C13 ⋊ D11×C29
HallC3×C11 ⋊ D13×C29
SylowC13 ⋊ C29×D33
SylowC11 ⋊ C29×D39
SylowC3 ⋊ C29×D143

Subgroups

subgroupG/H
center, hypercenterC29D429
commutator, cosocle, hypocenterC3×C11×C13C2×C29
FrattiniC1G
Fitting, socleC3×C11×C13×C29C2
LCSG ▷ C3×C11×C13
UCSC1 ◁ C29

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12441

Conjugacy classes & character table

6264 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24882, 16);