Finite Group Databasebeta

C9×C29×D71 #49150423

order37062
automorphism?
homologyAbelianization (H1) = C2×C9×C29 · Schur multiplier (H2) = C1

Aliases

direct productC9×C29×D71
unambiguous semidirect productC71⋊(C2×C9×C29)

Splittings

Fitting, HallC9×C29×C71 ⋊ C2
derived, SylowC71 ⋊ C2×C9×C29
HallC29×C71 ⋊ C2×C9
HallC9×C71 ⋊ C2×C29

Subgroups

subgroupG/H
center, hypercenterC9×C29D71
commutator, hypocenterC71C2×C9×C29
FrattiniC3C3×C29×D71
FittingC9×C29×C71C2
socleC3×C29×C71C2×C3
prime radicalC3×C29×D71C3
cosocleC3×C71C2×C3×C29
LCSG ▷ C71
UCSC1 ◁ C9×C29

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 18531

Conjugacy classes & character table

9657 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37062, 2);