Finite Group DatabasebetaFinite Group Databasebeta| order | 24321 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C121 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C67⋊C3)⋊C121 |
| unambiguous semidirect product | (C67⋊C121)⋊C3 |
| derived, Sylow | C67 ⋊ C3×C121 |
| Hall | C67⋊C121 ⋊ C3 |
| Hall | C67⋊C3 ⋊ C121 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C11 | (C67⋊C3)⋊C11 |
| commutator, hypocenter | C67 | C3×C121 |
| Fitting, socle, cosocle | C11×C67 | C3×C11 |
| prime radical | C11×C67⋊C3 | C11 |
| LCS | G ▷ C67 | |
| UCS | C1 ◁ C11 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8107 |
Polycyclic presentation:
3,11,67,11|b^11=d,c^a=c^37,c^b=c^64385 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24321, 2);