Finite Group Databasebeta

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C11×D169⋊C9 #45689494

order33462
automorphism?
homologyAbelianization (H1) = C2×C9×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×D169⋊C9
unambiguous semidirect productD169⋊(C9×C11)
unambiguous semidirect product(C169⋊C9)⋊(C2×C11)
unambiguous semidirect product(C11×D169)⋊C9

Splittings

derived, SylowC169 ⋊ C2×C9×C11
HallC11×C169⋊C9 ⋊ C2
HallC11×D169 ⋊ C9
HallC11×C169 ⋊ C2×C9
HallC169⋊C9 ⋊ C2×C11
HallD169 ⋊ C9×C11

Subgroups

subgroupG/H
center, hypercenterC3×C11D169⋊C3
commutator, hypocenterC169C2×C9×C11
FrattiniC3×C13C11×D13⋊C3
FittingC3×C11×C169C2×C3
socleC3×C11×C13D13⋊C3
prime radicalC3×C11×D169C3
cosocleC3×C169C2×C3×C11
LCSG ▷ C169
UCSC1 ◁ C3×C11

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16731

Conjugacy classes & character table

1122 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33462, 2);