Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C25×#100 ⋊ C2 |
| Sylow | C25 ⋊ #453 |
252 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 51 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 200 |
Polycyclic presentation:
2^6,5^2|c^2=ef,e^2=f,g^5=h,c^a=ce,d^a=df,e^a=ef,g^a=g^4h^4,h^a=h^4,c^b=cd,e^b=ef,d^c=df148 conjugacy classes — view the full character table.
| maximal subgroup of | D25×#453 |
| maximal normal subgroup of | D25×#453 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 374);