Finite Group Databasebeta

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C9×C11×Dic59 #37552482

order23364
automorphism?
homologyAbelianization (H1) = C4×C9×C11 · Schur multiplier (H2) = C1

Aliases

direct productC9×C11×Dic59
unambiguous semidirect productC59⋊(C4×C9×C11)

Splittings

derived, SylowC59 ⋊ C4×C9×C11
HallC9×C11×C59 ⋊ C4
HallC11×C59 ⋊ C4×C9
HallC9×C59 ⋊ C4×C11

Subgroups

subgroupG/H
center, hypercenterC2×C9×C11D59
commutator, hypocenterC59C4×C9×C11
FrattiniC2×C3C3×C11×D59
FittingC2×C9×C11×C59C2
socle, prime radicalC2×C3×C11×C59C2×C3
cosocleC2×C3×C59C2×C3×C11
LCSG ▷ C59
UCSC1 ◁ C2×C9×C11

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 23364

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, 2);