Finite Group DatabasebetaFinite Group Databasebeta| order | 24321 |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C11 |
| unambiguous semidirect product | C67⋊(C112⋊C3) |
| unambiguous semidirect product | C112⋊(C67⋊C3) |
| Fitting, socle, derived, Hall | C112×C67 ⋊ C3 |
| Sylow | C112 ⋊ C67⋊C3 |
| Sylow | C67 ⋊ C112⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C112×C67 | C3 |
| LCS | G ▷ C112×C67 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2211 |
Polycyclic presentation:
3,11^2,67|b^a=b^7c^10,c^a=b^2c^3,d^a=d^292705 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24321, 9);