Finite Group Databasebeta

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C9×C11×D107 #35234233

order21186
automorphism?
homologyAbelianization (H1) = C2×C9×C11 · Schur multiplier (H2) = C1

Aliases

direct productC9×C11×D107
unambiguous semidirect productC107⋊(C2×C9×C11)

Splittings

Fitting, HallC9×C11×C107 ⋊ C2
derived, SylowC107 ⋊ C2×C9×C11
HallC11×C107 ⋊ C2×C9
HallC9×C107 ⋊ C2×C11

Subgroups

subgroupG/H
center, hypercenterC9×C11D107
commutator, hypocenterC107C2×C9×C11
FrattiniC3C3×C11×D107
FittingC9×C11×C107C2
socleC3×C11×C107C2×C3
prime radicalC3×C11×D107C3
cosocleC3×C107C2×C3×C11
LCSG ▷ C107
UCSC1 ◁ C9×C11

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10593

Conjugacy classes & character table

5445 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21186, 2);