Finite Group DatabasebetaFinite Group Databasebeta| order | 25216 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C197 ⋊ #2855 |
564 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 189 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,b^2=ef,d^2=e,b^a=be,c^a=cf,d^a=dg,h^a=h^1966316 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25216, 12849);