Finite Group Databasebeta

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C9×C11⋊C5×C67 #45684237

order33165
automorphism?
homologyAbelianization (H1) = C5×C9×C67 · Schur multiplier (H2) = C1

Aliases

direct productC9×C11⋊C5×C67
unambiguous semidirect productC11⋊(C5×C9×C67)
unambiguous semidirect product(C9×C11)⋊(C5×C67)
unambiguous semidirect product(C9×C11×C67)⋊C5

Splittings

Fitting, HallC9×C11×C67 ⋊ C5
derived, SylowC11 ⋊ C5×C9×C67
HallC11×C67 ⋊ C5×C9
HallC9×C11 ⋊ C5×C67

Subgroups

subgroupG/H
center, hypercenterC9×C67C11⋊C5
commutator, hypocenterC11C5×C9×C67
FrattiniC3C3×C11⋊C5×C67
FittingC9×C11×C67C5
socleC3×C11×C67C3×C5
prime radicalC3×C11⋊C5×C67C3
cosocleC3×C11C3×C5×C67
LCSG ▷ C11
UCSC1 ◁ C9×C67

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6633

Conjugacy classes & character table

4221 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33165, 3);