Finite Group DatabasebetaFinite Group Databasebeta| order | 24682 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C41⋊(D43⋊C7) |
| unambiguous semidirect product | (C43⋊C7)⋊D41 |
| unambiguous semidirect product | D1763⋊C7 |
| Fitting, socle, derived, Hall | C41×C43 ⋊ C2×C7 |
| Hall | C41×C43⋊C7 ⋊ C2 |
| Hall | D1763 ⋊ C7 |
| Hall | C43⋊C7 ⋊ D41 |
| Sylow | C43 ⋊ C7×D41 |
| Sylow | C41 ⋊ D43⋊C7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C41×C43 | C2×C7 |
| LCS | G ▷ C41×C43 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1763 |
Polycyclic presentation:
2,7,41,43|c^a=c^40,d^a=d^42,d^b=d^41277 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24682, 12);