Finite Group DatabasebetaFinite Group Databasebeta| order | 33300 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | (C5⋊(#66526⋊C2))⋊D5 |
| Fitting, socle, derived, Hall | C52×C37 ⋊ C22×C9 |
| Hall | C52×#66526 ⋊ C22 |
| Hall | (C5⋊D5)⋊D37 ⋊ C9 |
| Hall | #66526 ⋊ D52 |
| Sylow | C37 ⋊ C9×D52 |
| Sylow | C52 ⋊ C2×#66526⋊C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C52×C37 | C22×C9 |
| prime radical | (C5⋊(D37⋊C3))⋊D5 | C3 |
| cosocle | C52×C37⋊C3 | C22×C3 |
| LCS | G ▷ C52×C37 | |
| UCS | C1 | |
144 conjugacy classes of subgroups.
| transitive degree | μt(G) = 370 |
Polycyclic presentation:
2^2,3^2,5^2,37|c^3=d,e^a=e^4,g^a=g^36,e^b=e^4,f^b=f^4,g^c=g^16,g^d=g^26172 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33300, 447);