Finite Group DatabasebetaFinite Group Databasebeta| order | 17919 |
| automorphism | ? |
| homology | Abelianization (H1) = C9×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×#13108656 |
| derived, Sylow | C181 ⋊ C9×C11 |
| Hall | C11×C181 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C11 | C181⋊C3 |
| commutator, hypocenter | C181 | C9×C11 |
| Frattini | C3 | C11×C181⋊C3 |
| Fitting, socle, prime radical | C3×C11×C181 | C3 |
| cosocle | C3×C181 | C3×C11 |
| LCS | G ▷ C181 | |
| UCS | C1 ◁ C3×C11 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17919 |
2079 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C11×#13108656, C11×#13108656⋊C2, D11×#13108656, … |
| maximal normal subgroup of | C2×C11×#13108656, C11×#13108656⋊C2, D11×#13108656, … |
| maximal quotient of | C2×C11×#13108656 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17919, 2);