Finite Group DatabasebetaFinite Group Databasebeta| order | 29988 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting, socle, derived | C3×C72×C17 ⋊ C22×C3 |
| Hall | C3×C17×#3861 ⋊ C22 |
| Hall | C72×C17 ⋊ C2×C3×D3 |
| Hall | C3×#3861 ⋊ C2×D17 |
| Sylow | C72 ⋊ C3×D3×D17 |
| Sylow | C17 ⋊ #64423⋊D3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C72×C17 | C22×C3 |
| LCS | G ▷ C3×C72×C17 | |
| UCS | C1 | |
230 conjugacy classes of subgroups; only the 35 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 35 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 714 |
Polycyclic presentation:
2^2,3^2,7^2,17|e^a=e^6,g^a=g^16,d^b=d^2,e^b=e^6,f^b=f^6,e^c=e^2,f^c=f^2300 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29988, 474);