Finite Group Databasebeta

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C2×C9×D11×C59 #37552503

order23364
automorphism?
homologyAbelianization (H1) = C22×C9×C59 · Schur multiplier (H2) = C2

Aliases

direct productC2×C9×D11×C59
unambiguous semidirect productC11⋊(C22×C9×C59)
unambiguous semidirect product(C2×C11)⋊(C2×C9×C59)

Splittings

FittingC2×C9×C11×C59 ⋊ C2
derived, SylowC11 ⋊ C22×C9×C59
HallC9×C11×C59 ⋊ C22
HallC11×C59 ⋊ C22×C9
HallC9×C11 ⋊ C22×C59

Subgroups

subgroupG/H
center, hypercenterC2×C9×C59D11
commutator, hypocenterC11C22×C9×C59
FrattiniC3C2×C3×D11×C59
FittingC2×C9×C11×C59C2
socleC2×C3×C11×C59C2×C3
prime radicalC2×C3×D11×C59C3
cosocleC3×C11C22×C3×C59
LCSG ▷ C11
UCSC1 ◁ C2×C9×C59

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11682

Conjugacy classes & character table

7434 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23364, 23);