Finite Group DatabasebetaFinite Group Databasebeta| order | 24684 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C3×D17×D121 |
| unambiguous semidirect product | (C17×D121)⋊(C2×C3) |
| unambiguous semidirect product | (D17×C121)⋊(C2×C3) |
| unambiguous semidirect product | D2057⋊(C2×C3) |
| Fitting, Hall | C3×C17×C121 ⋊ C22 |
| derived, Hall | C17×C121 ⋊ C22×C3 |
| Hall | C3×C121 ⋊ C2×D17 |
| Sylow | C121 ⋊ C2×C3×D17 |
| Hall | C3×C17 ⋊ C2×D121 |
| Sylow | C17 ⋊ C2×C3×D121 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D17×D121 |
| commutator, cosocle, hypocenter | C17×C121 | C22×C3 |
| Frattini | C11 | C3×D11×D17 |
| Fitting | C3×C17×C121 | C22 |
| socle | C3×C11×C17 | C2×D11 |
| LCS | G ▷ C17×C121 | |
| UCS | C1 ◁ C3 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6171 |
1860 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24684, 12);