Finite Group DatabasebetaFinite Group Databasebeta| order | 25216 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | #335×C197 ⋊ C2 |
| Sylow | C197 ⋊ C8×D8 |
196 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 73 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 12608 |
Polycyclic presentation:
2^7,197|a^2=e,c^2=e,d^2=f,e^2=g,b^a=bd,d^a=df,d^b=df,h^b=h^196,h^c=h^1962800 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25216, 3304);