Finite Group Databasebeta

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C5×(C67⋊C9)⋊C11 #45684239

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

Aliases

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

Splittings

derived, SylowC67 ⋊ C5×C9×C11
HallC5×C67⋊C11 ⋊ C9
HallC5×C67⋊C9 ⋊ C11
HallC67⋊C11 ⋊ C5×C9
HallC67⋊C9 ⋊ C5×C11
HallC5×C67 ⋊ C9×C11

Subgroups

subgroupG/H
center, hypercenterC3×C5(C67⋊C3)⋊C11
commutator, hypocenterC67C5×C9×C11
FrattiniC3C5×(C67⋊C3)⋊C11
Fitting, socleC3×C5×C67C3×C11
prime radicalC3×C5×C67⋊C11C3
cosocleC3×C67C3×C5×C11
LCSG ▷ C67
UCSC1 ◁ C3×C5

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3015

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33165, 5);