Finite Group DatabasebetaFinite Group Databasebeta| order | 33300 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C5 |
| unambiguous semidirect product | D37⋊(C3⋊((C5⋊D5)⋊C3)) |
| unambiguous semidirect product | (D37⋊(C52⋊C3))⋊D3 |
| Fitting, socle, derived | C3×C52×C37 ⋊ C22×C3 |
| Hall | C3×C52⋊(C37⋊C3) ⋊ C22 |
| Hall | C52×C37 ⋊ C2×C3×D3 |
| Sylow | C37 ⋊ C2×C3⋊((C5⋊D5)⋊C3) |
| Sylow | C52 ⋊ D3×D37⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C52×C37 | C22×C3 |
| LCS | G ▷ C3×C52×C37 | |
| UCS | C1 | |
128 conjugacy classes of subgroups; only the 23 normal subgroups are shown.
This group has 128 conjugacy classes of subgroups — too many to draw. Only its 23 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1665 |
Polycyclic presentation:
2^2,3^2,5^2,37|g^a=g^36,d^b=d^2,e^b=e^4,f^b=f^4,e^c=ef^3,f^c=e^4f^3,g^c=g^26276 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33300, 527);