Finite Group Databasebeta

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C11×Dic9×C59 #37552485

order23364
automorphism?
homologyAbelianization (H1) = C4×C11×C59 · Schur multiplier (H2) = C1

Aliases

direct productC11×Dic9×C59
unambiguous semidirect productC9⋊(C4×C11×C59)

Splittings

derived, SylowC9 ⋊ C4×C11×C59
HallC9×C11×C59 ⋊ C4
HallC9×C59 ⋊ C4×C11
HallC9×C11 ⋊ C4×C59

Subgroups

subgroupG/H
center, hypercenterC2×C11×C59D9
commutator, hypocenterC9C4×C11×C59
FrattiniC2×C3D3×C11×C59
FittingC2×C9×C11×C59C2
socle, prime radicalC2×C3×C11×C59D3
cosocleC2×C9C2×C11×C59
LCSG ▷ C9
UCSC1 ◁ C2×C11×C59

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 23364

Conjugacy classes & character table

7788 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23364, 5);