Finite Group Databasebeta

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C2×C9×C11×D59 #37552504

order23364
automorphism?
homologyAbelianization (H1) = C22×C9×C11 · Schur multiplier (H2) = C2

Aliases

direct productC2×C9×C11×D59
unambiguous semidirect productC59⋊(C22×C9×C11)
unambiguous semidirect product(C2×C59)⋊(C2×C9×C11)

Splittings

FittingC2×C9×C11×C59 ⋊ C2
derived, SylowC59 ⋊ C22×C9×C11
HallC9×C11×C59 ⋊ C22
HallC11×C59 ⋊ C22×C9
HallC9×C59 ⋊ C22×C11

Subgroups

subgroupG/H
center, hypercenterC2×C9×C11D59
commutator, hypocenterC59C22×C9×C11
FrattiniC3C2×C3×C11×D59
FittingC2×C9×C11×C59C2
socleC2×C3×C11×C59C2×C3
prime radicalC2×C3×C11×D59C3
cosocleC3×C59C22×C3×C11
LCSG ▷ C59
UCSC1 ◁ C2×C9×C11

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11682

Conjugacy classes & character table

6138 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23364, 24);