Finite Group DatabasebetaFinite Group Databasebeta| order | 33300 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C5 |
| unambiguous semidirect product | C9⋊#16814881 |
| Fitting, derived, Hall | C52×C9×C37 ⋊ C4 |
| Hall | C52×C37 ⋊ Dic9 |
| Hall | C9×C37 ⋊ #1044 |
| Hall | C52×C9 ⋊ #3866 |
| Sylow | C37 ⋊ C9⋊#1044 |
| Sylow | C52 ⋊ C9⋊#3866 |
| Sylow | C9 ⋊ #16814881 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C52×C9×C37 | C4 |
| Frattini | C3 | C3⋊#16814881 |
| socle | C3×C52×C37 | Dic3 |
| prime radical | C3×C5⋊D185 | D3 |
| cosocle | C9×C5⋊D185 | C2 |
| LCS | G ▷ C52×C9×C37 | |
| UCS | C1 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3330 |
Polycyclic presentation:
2^2,3,5^2,37,3|a^2=b,c^3=g^2,c^a=c^2g,d^a=d^2,e^a=e^3,f^a=f^31,g^a=g^2,d^b=d^4,e^b=e^4,f^b=f^362091 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33300, 309);