Finite Group DatabasebetaFinite Group Databasebeta| order | 29988 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | D17×C3⋊(D49⋊C3) |
| unambiguous semidirect product | (C3×D17)⋊(D49⋊C3) |
| unambiguous semidirect product | (D17×C49⋊C3)⋊D3 |
| unambiguous semidirect product | (D17×D147)⋊C3 |
| Fitting, derived | C3×C17×C49 ⋊ C22×C3 |
| Hall | C3×C17×C49⋊C3 ⋊ C22 |
| Hall | C17×C49 ⋊ C2×C3×D3 |
| Hall | C3×C49⋊C3 ⋊ C2×D17 |
| Sylow | C49 ⋊ C3×D3×D17 |
| Sylow | C17 ⋊ C2×C3⋊(D49⋊C3) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C3×C17×C49 | C22×C3 |
| Frattini | C7 | D17×C3⋊AGL(1,𝔽7) |
| socle | C3×C7×C17 | C2×AGL(1,𝔽7) |
| LCS | G ▷ C3×C17×C49 | |
| UCS | C1 | |
132 conjugacy classes of subgroups; only the 32 normal subgroups are shown.
This group has 132 conjugacy classes of subgroups — too many to draw. Only its 32 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 2499 |
330 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29988, 66);