Finite Group Databasebeta

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C11×D157⋊C9 #44527263

order31086
automorphism?
homologyAbelianization (H1) = C2×C9×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×D157⋊C9
unambiguous semidirect productD157⋊(C9×C11)
unambiguous semidirect product(C157⋊C9)⋊(C2×C11)
unambiguous semidirect product(C11×D157)⋊C9

Splittings

derived, SylowC157 ⋊ C2×C9×C11
HallC11×C157⋊C9 ⋊ C2
HallC11×D157 ⋊ C9
HallC11×C157 ⋊ C2×C9
HallC157⋊C9 ⋊ C2×C11
HallD157 ⋊ C9×C11

Subgroups

subgroupG/H
center, hypercenterC3×C11D157⋊C3
commutator, hypocenterC157C2×C9×C11
FrattiniC3C11×D157⋊C3
Fitting, socleC3×C11×C157C2×C3
prime radicalC3×C11×D157C3
cosocleC3×C157C2×C3×C11
LCSG ▷ C157
UCSC1 ◁ C3×C11

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15543

Conjugacy classes & character table

1056 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31086, 10);