Finite Group Databasebeta

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C41×D429 #47976014

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

Aliases

direct productC41×D429
unambiguous semidirect productC3⋊(C41×D143)
unambiguous semidirect productC11⋊(C41×D39)
unambiguous semidirect productC13⋊(C41×D33)

Splittings

Fitting, socle, HallC3×C11×C13×C41 ⋊ C2
derived, HallC3×C11×C13 ⋊ C2×C41
HallC11×C13×C41 ⋊ D3
HallC3×C13×C41 ⋊ D11
HallC3×C11×C41 ⋊ D13
HallC13×C41 ⋊ D33
HallC11×C41 ⋊ D39
HallC11×C13 ⋊ D3×C41
HallC3×C41 ⋊ D143
HallC3×C13 ⋊ D11×C41
HallC3×C11 ⋊ D13×C41
SylowC13 ⋊ C41×D33
SylowC11 ⋊ C41×D39
SylowC3 ⋊ C41×D143

Subgroups

subgroupG/H
center, hypercenterC41D429
commutator, cosocle, hypocenterC3×C11×C13C2×C41
FrattiniC1G
Fitting, socleC3×C11×C13×C41C2
LCSG ▷ C3×C11×C13
UCSC1 ◁ C41

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17589

Conjugacy classes & character table

8856 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35178, 16);