Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C52 ⋊ C2×M32 |
207 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 207 conjugacy classes of subgroups — too many to draw. Only its 68 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|a^2=d,b^2=e,d^2=e,e^2=f,c^a=cf,g^a=g^2,h^b=h^4,g^d=g^4112 conjugacy classes — view the full character table.
| maximal subgroup of | #72220672, #72220674, #72220677, … |
| maximal normal subgroup of | #72220672, #72220674, #72220677, … |
| maximal quotient of | #72242231 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 5950);