Finite Group DatabasebetaFinite Group Databasebeta| order | 36224 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C22×C42 |
No aliases for this group.
| Fitting | #390×C283 ⋊ C2 |
| Sylow | C283 ⋊ #2375 |
688 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 688 conjugacy classes of subgroups — too many to draw. Only its 173 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,b^a=be,c^a=cf,d^a=def,c^b=cef,d^b=de,h^d=h^2823986 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36224, 7647);