Finite Group DatabasebetaFinite Group Databasebeta| order | 36300 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C5 |
| unambiguous semidirect product | C3⋊#27130863 |
| derived, Hall | C3×C5×#10597245 ⋊ C4 |
| Hall | C5×#10597245 ⋊ Dic3 |
| Hall | C3×C112 ⋊ #1039 |
| Sylow | C112 ⋊ C3⋊#1039 |
| Sylow | C3 ⋊ #27130863 |
152 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 41 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 660 |
Polycyclic presentation:
2,3,5^2,11^2,2|a^2=g,b^a=b^2,c^a=c^4,d^a=d^4,e^a=e^3f^3,f^a=ef^8,e^c=e^4f^8,f^c=f^3468 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36300, 416);