Finite Group Databasebeta

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C9×C11×D167 #45683389

order33066
automorphism?
homologyAbelianization (H1) = C2×C9×C11 · Schur multiplier (H2) = C1

Aliases

direct productC9×C11×D167
unambiguous semidirect productC167⋊(C2×C9×C11)

Splittings

Fitting, HallC9×C11×C167 ⋊ C2
derived, SylowC167 ⋊ C2×C9×C11
HallC11×C167 ⋊ C2×C9
HallC9×C167 ⋊ C2×C11

Subgroups

subgroupG/H
center, hypercenterC9×C11D167
commutator, hypocenterC167C2×C9×C11
FrattiniC3C3×C11×D167
FittingC9×C11×C167C2
socleC3×C11×C167C2×C3
prime radicalC3×C11×D167C3
cosocleC3×C167C2×C3×C11
LCSG ▷ C167
UCSC1 ◁ C9×C11

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16533

Conjugacy classes & character table

8415 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33066, 2);