Finite Group DatabasebetaFinite Group Databasebeta| order | 24402 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C49 · Schur multiplier (H2) = C1 |
| direct product | C3×C49×D83 |
| unambiguous semidirect product | C83⋊(C2×C3×C49) |
| Fitting, Hall | C3×C49×C83 ⋊ C2 |
| derived, Sylow | C83 ⋊ C2×C3×C49 |
| Hall | C49×C83 ⋊ C2×C3 |
| Hall | C3×C83 ⋊ C2×C49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C49 | D83 |
| commutator, hypocenter | C83 | C2×C3×C49 |
| Frattini | C7 | C3×C7×D83 |
| Fitting | C3×C49×C83 | C2 |
| socle | C3×C7×C83 | C2×C7 |
| prime radical | C3×C7×D83 | C7 |
| cosocle | C7×C83 | C2×C3×C7 |
| LCS | G ▷ C83 | |
| UCS | C1 ◁ C3×C49 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 12201 |
6321 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24402, 3);