Finite Group DatabasebetaFinite Group Databasebeta| order | 25472 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C8×Q8×C199 ⋊ C2 |
| Sylow | C199 ⋊ #1583 |
166 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 69 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 12736 |
Polycyclic presentation:
2^7,199|a^2=e,b^2=f,c^2=e,d^2=f,e^2=g,b^a=bd,c^a=cg,d^a=df,h^a=h^198,d^b=df3998 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25472, 3353);