Finite Group DatabasebetaFinite Group Databasebeta| order | 10901 |
| automorphism | ? |
| homology | Abelianization (H1) = C11 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C991⋊C11 |
| Fitting, socle, derived, Sylow | C991 ⋊ C11 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C991 | C11 |
| LCS | G ▷ C991 | |
| UCS | C1 | |
4 conjugacy classes of subgroups.
Polycyclic presentation:
11,991|b^a=b^118101 conjugacy classes — view the full character table.
| maximal subgroup of | D991⋊C11, C2×C991⋊C11, (C991⋊C3)⋊C11, … |
| maximal normal subgroup of | D991⋊C11, C2×C991⋊C11, (C991⋊C3)⋊C11, … |
| maximal quotient of | C2×C991⋊C11, C3×C991⋊C11 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10901, 1);