Finite Group DatabasebetaFinite Group Databasebeta| order | 17444 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D49×D89 |
| unambiguous semidirect product | (C89×D49)⋊C2 |
| unambiguous semidirect product | (C49×D89)⋊C2 |
| unambiguous semidirect product | D4361⋊C2 |
| Fitting, derived, Hall | C49×C89 ⋊ C22 |
| Sylow | C89 ⋊ C2×D49 |
| Sylow | C49 ⋊ C2×D89 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C49×C89 | C22 |
| Frattini | C7 | D7×D89 |
| socle | C7×C89 | C2×D7 |
| LCS | G ▷ C49×C89 | |
| UCS | C1 | |
30 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4361 |
1196 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17444, 8);