Finite Group Databasebeta

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C11×C22⋊#66524 #28410818

order14652
automorphism?
homologyAbelianization (H1) = C9×C11 · Schur multiplier (H2) = C2

Aliases

direct productC11×C22⋊#66524
unambiguous semidirect productC22⋊(C11×#66524)
unambiguous semidirect product(C22×C11)⋊#66524

Splittings

derived, HallC22×C37 ⋊ C9×C11
HallC22×C11×C37 ⋊ C9
HallC11×C37 ⋊ C22⋊C9
HallC22×C11 ⋊ #66524
SylowC37 ⋊ C11×C22⋊C9
SylowC22 ⋊ C11×#66524

Subgroups

subgroupG/H
center, hypercenterC3×C11C22⋊(C37⋊C3)
commutator, hypocenterC22×C37C9×C11
FrattiniC3C11×C22⋊(C37⋊C3)
Fitting, socle, prime radicalC22×C3×C11×C37C3
cosocleC22×C3×C37C3×C11
LCSG ▷ C22×C37
UCSC1 ◁ C3×C11

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7326

Conjugacy classes & character table

1716 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14652, 33);