Finite Group DatabasebetaFinite Group Databasebeta| order | 29988 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D153⋊D49 |
| unambiguous semidirect product | D441⋊D17 |
| unambiguous semidirect product | D833⋊D9 |
| Fitting, derived, Hall | C9×C17×C49 ⋊ C22 |
| Hall | C17×C49 ⋊ C2×D9 |
| Hall | C9×C49 ⋊ C2×D17 |
| Hall | C9×C17 ⋊ C2×D49 |
| Sylow | C49 ⋊ D9×D17 |
| Sylow | C17 ⋊ D9×D49 |
| Sylow | C9 ⋊ D17×D49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C9×C17×C49 | C22 |
| Frattini | C3×C7 | D21⋊D17 |
| socle | C3×C7×C17 | D3×D7 |
| LCS | G ▷ C9×C17×C49 | |
| UCS | C1 | |
90 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7497 |
Polycyclic presentation:
2^2,3,7,17,3,7|c^3=f^2,d^7=g^6,d^a=d^6g,e^a=e^16,g^a=g^6,c^b=c^2f,d^b=d^6g,f^b=f^2,g^b=g^61932 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29988, 30);