Finite Group DatabasebetaFinite Group Databasebeta| order | 33300 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C5 |
| unambiguous semidirect product | C3⋊(Dic37⋊(C52⋊C3)) |
| unambiguous semidirect product | Dic111⋊(C52⋊C3) |
| derived | C3×C52×C37 ⋊ C3×C4 |
| Hall | C3×C52⋊(C37⋊C3) ⋊ C4 |
| Hall | C52×C37 ⋊ C3×Dic3 |
| Sylow | C37 ⋊ Dic3×C52⋊C3 |
| Sylow | C52 ⋊ C3⋊(Dic37⋊C3) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C3⋊(D37⋊(C52⋊C3)) |
| commutator, hypocenter | C3×C52×C37 | C3×C4 |
| Fitting, socle, cosocle | C2×C3×C52×C37 | C2×C3 |
| prime radical | C2×C3×C52⋊(C37⋊C3) | C2 |
| LCS | G ▷ C3×C52×C37 | |
| UCS | C1 ◁ C2 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6660 |
Polycyclic presentation:
2,3^2,5^2,37,2|a^2=g,c^a=c^2,f^a=f^36,d^b=d^3e^2,e^b=de,f^b=f^26966 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33300, 389);