Finite Group DatabasebetaFinite Group Databasebeta| order | 29988 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D147⋊D51 |
| Fitting, derived, Hall | C32×C17×C49 ⋊ C22 |
| Hall | C17×C49 ⋊ D32 |
| Hall | C32×C49 ⋊ C2×D17 |
| Hall | C32×C17 ⋊ C2×D49 |
| Sylow | C49 ⋊ D3×D51 |
| Sylow | C17 ⋊ (C3⋊D3)⋊D49 |
| Sylow | C32 ⋊ D17×D49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C32×C17×C49 | C22 |
| Frattini | C7 | D21⋊D51 |
| socle | C32×C7×C17 | C2×D7 |
| LCS | G ▷ C32×C17×C49 | |
| UCS | C1 | |
132 conjugacy classes of subgroups; only the 34 normal subgroups are shown.
This group has 132 conjugacy classes of subgroups — too many to draw. Only its 34 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 4998 |
Polycyclic presentation:
2^2,3^2,7,17,7|e^7=g^6,c^a=c^2,d^a=d^2,f^a=f^16,d^b=d^2,e^b=e^6g,g^b=g^61953 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29988, 108);