Finite Group DatabasebetaFinite Group Databasebeta| order | 29988 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting, socle | C3×C72×C17 ⋊ C2×D3 |
| derived, Hall | C3×C17×#3862 ⋊ C22 |
| Hall | C72×C17 ⋊ D32 |
| Hall | C3×#3862 ⋊ C2×D17 |
| Sylow | C72 ⋊ (C3⋊D3)⋊D17 |
| Sylow | C17 ⋊ #64418⋊D3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C3×C17×#3862 | C22 |
| Fitting, socle | C3×C72×C17 | C2×D3 |
| LCS | G ▷ C3×C17×#3862 | |
| UCS | C1 | |
146 conjugacy classes of subgroups; only the 19 normal subgroups are shown.
This group has 146 conjugacy classes of subgroups — too many to draw. Only its 19 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:
2^2,3^2,17,7^2|c^a=c^2,e^a=e^16,g^a=f^3g^6,c^b=c^2,d^b=d^2,f^b=f^6,g^b=f^4g,f^c=f^4g^4,g^c=g^2351 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29988, 421);