Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×C52×C8 ⋊ C22 |
| Sylow | C52 ⋊ C2×#131 |
608 conjugacy classes of subgroups; only the 186 normal subgroups are shown.
This group has 608 conjugacy classes of subgroups — too many to draw. Only its 186 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 80 |
Polycyclic presentation:
2^6,5^2|d^2=e,e^2=f,c^a=cf,g^a=g^4,c^b=cf,h^b=h^4184 conjugacy classes — view the full character table.
| maximal subgroup of | #72220721, #72220804, #72220806, … |
| maximal normal subgroup of | #72220721, #72220804, #72220806, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 8112);