Finite Group DatabasebetaFinite Group Databasebeta| order | 25472 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C199 ⋊ #1833 |
172 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 81 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 6368 |
Polycyclic presentation:
2^7,199|a^2=f,b^2=e,c^2=d,e^2=g,b^a=bd,c^a=ce,d^a=dg,h^a=h^198,f^b=fg,h^b=h^198,f^c=fg,h^c=h^1982804 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25472, 4635);