Finite Group Databasebeta

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C9×Dic11×C59 #37552483

order23364
automorphism?
homologyAbelianization (H1) = C4×C9×C59 · Schur multiplier (H2) = C1

Aliases

direct productC9×Dic11×C59
unambiguous semidirect productC11⋊(C4×C9×C59)

Splittings

derived, SylowC11 ⋊ C4×C9×C59
HallC9×C11×C59 ⋊ C4
HallC11×C59 ⋊ C4×C9
HallC9×C11 ⋊ C4×C59

Subgroups

subgroupG/H
center, hypercenterC2×C9×C59D11
commutator, hypocenterC11C4×C9×C59
FrattiniC2×C3C3×D11×C59
FittingC2×C9×C11×C59C2
socle, prime radicalC2×C3×C11×C59C2×C3
cosocleC2×C3×C11C2×C3×C59
LCSG ▷ C11
UCSC1 ◁ C2×C9×C59

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 23364

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, 3);