Finite Group DatabasebetaFinite Group Databasebeta| order | 36224 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4 |
No aliases for this group.
| Fitting | #381×C283 ⋊ C2 |
| Sylow | C283 ⋊ #2280 |
1088 conjugacy classes of subgroups; only the 245 normal subgroups are shown.
This group has 1088 conjugacy classes of subgroups — too many to draw. Only its 245 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 9056 |
Polycyclic presentation:
2^7,283|a^2=g,d^2=e,b^a=be,c^a=cf,h^c=h^282,h^d=h^2824004 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36224, 6890);