Finite Group Databasebeta

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C9×C11×D113 #36375406

order22374
automorphism?
homologyAbelianization (H1) = C2×C9×C11 · Schur multiplier (H2) = C1

Aliases

direct productC9×C11×D113
unambiguous semidirect productC113⋊(C2×C9×C11)

Splittings

Fitting, HallC9×C11×C113 ⋊ C2
derived, SylowC113 ⋊ C2×C9×C11
HallC11×C113 ⋊ C2×C9
HallC9×C113 ⋊ C2×C11

Subgroups

subgroupG/H
center, hypercenterC9×C11D113
commutator, hypocenterC113C2×C9×C11
FrattiniC3C3×C11×D113
FittingC9×C11×C113C2
socleC3×C11×C113C2×C3
prime radicalC3×C11×D113C3
cosocleC3×C113C2×C3×C11
LCSG ▷ C113
UCSC1 ◁ C9×C11

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11187

Conjugacy classes & character table

5742 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22374, 2);