Finite Group Databasebeta

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C5×C9×C67⋊C11 #45684236

order33165
automorphism?
homologyAbelianization (H1) = C5×C9×C11 · Schur multiplier (H2) = C1

Aliases

direct productC5×C9×C67⋊C11
unambiguous semidirect product(C9×C67)⋊(C5×C11)
unambiguous semidirect product(C5×C9×C67)⋊C11

Splittings

Fitting, HallC5×C9×C67 ⋊ C11
derived, SylowC67 ⋊ C5×C9×C11
HallC9×C67 ⋊ C5×C11
HallC5×C67 ⋊ C9×C11

Subgroups

subgroupG/H
center, hypercenterC5×C9C67⋊C11
commutator, hypocenterC67C5×C9×C11
FrattiniC3C3×C5×C67⋊C11
FittingC5×C9×C67C11
socleC3×C5×C67C3×C11
prime radicalC3×C5×C67⋊C11C3
cosocleC3×C67C3×C5×C11
LCSG ▷ C67
UCSC1 ◁ C5×C9

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3015

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33165, 2);