Finite Group DatabasebetaFinite Group Databasebeta| order | 33300 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #3874⋊(D37⋊C3) |
| unambiguous semidirect product | (#3874⋊D37)⋊C3 |
| Fitting, socle, Hall | C52×C37 ⋊ C2×C3×D3 |
| derived | C37×C52⋊C3 ⋊ C22×C3 |
| Hall | C52⋊C3×C37⋊C3 ⋊ C22 |
| Sylow | C37 ⋊ C3×#3874⋊C2 |
| Sylow | C52 ⋊ D3×D37⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C37×C52⋊C3 | C22×C3 |
| Fitting, socle | C52×C37 | C2×C3×D3 |
| LCS | G ▷ C37×C52⋊C3 | |
| UCS | C1 | |
128 conjugacy classes of subgroups; only the 20 normal subgroups are shown.
This group has 128 conjugacy classes of subgroups — too many to draw. Only its 20 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 555 |
Polycyclic presentation:
2^2,3^2,37,5^2|d^a=d^2,e^a=e^36,f^a=fg,g^a=g^4,d^b=d^2,f^b=f^4g^4,e^c=e^26,f^d=g,g^d=f^4g^4120 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33300, 432);