Finite Group DatabasebetaFinite Group Databasebeta| order | 29988 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C49⋊#10597479 |
| Fitting, derived, Hall | C32×C17×C49 ⋊ C4 |
| Hall | C17×C49 ⋊ #157 |
| Hall | C32×C49 ⋊ #595 |
| Hall | C32×C17 ⋊ Dic49 |
| Sylow | C49 ⋊ #10597479 |
| Sylow | C17 ⋊ C49⋊#157 |
| Sylow | C32 ⋊ C49⋊#595 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C32×C17×C49 | C4 |
| Frattini | C7 | C7⋊#10597479 |
| socle | C32×C7×C17 | Dic7 |
| prime radical | C7×C3⋊D51 | D7 |
| cosocle | C49×C3⋊D51 | C2 |
| LCS | G ▷ C32×C17×C49 | |
| UCS | C1 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4998 |
Polycyclic presentation:
2^2,3^2,7,17,7|a^2=b,e^7=g^6,c^a=cd,d^a=cd^2,e^a=e^6g,f^a=f^13,g^a=g^6,c^b=c^2,d^b=d^2,f^b=f^161914 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29988, 114);