Finite Group DatabasebetaFinite Group Databasebeta| order | 29988 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C7 |
No aliases for this group.
| derived, Hall | C17×#89205 ⋊ C4 |
| Hall | C72×C17 ⋊ Dic9 |
| Hall | #89205 ⋊ Dic17 |
| Sylow | C72 ⋊ Dic153 |
| Sylow | C17 ⋊ #13183544 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, hypocenter | C17×#89205 | C4 |
| Frattini | C3 | #23756207 |
| Fitting, socle | C3×C72×C17 | Dic3 |
| prime radical | C3×C17×C7⋊D7 | D3 |
| cosocle | C17×#11725078 | C2 |
| LCS | G ▷ C17×#89205 | |
| UCS | C1 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2142 |
Polycyclic presentation:
2^2,3,17,7^2,3|a^2=b,c^3=g^2,c^a=c^2g,d^a=d^16,e^a=e^3f^4,f^a=ef^4,g^a=g^2,e^b=e^6,f^b=f^6,e^c=e^2f^6,f^c=f^4360 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29988, 199);