Finite Group DatabasebetaFinite Group Databasebeta| order | 29988 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C3×C7 |
| unambiguous semidirect product | C3⋊(C3⋊#16809726) |
| Fitting, socle, derived, Hall | C32×C72×C17 ⋊ C4 |
| Hall | C72×C17 ⋊ C3⋊Dic3 |
| Hall | C32×C72 ⋊ Dic17 |
| Hall | C32×C17 ⋊ #5997 |
| Sylow | C72 ⋊ C3⋊Dic51 |
| Sylow | C17 ⋊ C3⋊(C3⋊#5997) |
| Sylow | C32 ⋊ #16809726 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C32×C72×C17 | C4 |
| prime radical, cosocle | C32×C17×C7⋊D7 | C2 |
| LCS | G ▷ C32×C72×C17 | |
| UCS | C1 | |
168 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2142 |
Polycyclic presentation:
2^2,3^2,7^2,17|a^2=b,c^a=c^2,d^a=d^2,e^a=e^4f^3,f^a=e^6f^3,g^a=g^16,e^b=e^6,f^b=f^61992 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29988, 621);