Finite Group DatabasebetaFinite Group Databasebeta| order | 33300 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊Dic2775 |
| derived, Hall | C32×C25×C37 ⋊ C4 |
| Hall | C25×C37 ⋊ C3⋊Dic3 |
| Hall | C32×C37 ⋊ Dic25 |
| Hall | C32×C25 ⋊ Dic37 |
| Sylow | C37 ⋊ C3⋊Dic75 |
| Sylow | C25 ⋊ C3⋊Dic111 |
| Sylow | C32 ⋊ Dic925 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C3⋊D2775 |
| commutator, hypocenter | C32×C25×C37 | C4 |
| Frattini | C2×C5 | C3⋊D555 |
| Fitting, cosocle | C2×C32×C25×C37 | C2 |
| socle, prime radical | C2×C32×C5×C37 | D5 |
| LCS | G ▷ C32×C25×C37 | |
| UCS | C1 ◁ C2 | |
108 conjugacy classes of subgroups.
| transitive degree | μt(G) = 33300 |
Polycyclic presentation:
2,3^2,5,37,2,5|a^2=f,d^5=g^4,b^a=b^2,c^a=c^2,d^a=d^4g,e^a=e^36,g^a=g^48328 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33300, 76);