Finite Group DatabasebetaFinite Group Databasebeta| order | 25472 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C199 ⋊ #2127 |
286 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 286 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) = 3184 |
Polycyclic presentation:
2^7,199|a^2=e,d^2=g,b^a=bd,d^a=df,f^a=fg,h^a=h^198,c^b=cg,d^b=dg,e^b=efg,e^d=eg2201 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25472, 6179);