Finite Group DatabasebetaFinite Group Databasebeta| order | 25664 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C22⋊C8×C401 ⋊ C2 |
| Sylow | C401 ⋊ #435 |
124 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 53 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 12832 |
Polycyclic presentation:
2^6,401|a^2=e,c^2=e,e^2=f,b^a=bd,c^a=cf,g^c=g^4004028 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25664, 617);