Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C52 ⋊ #388 |
472 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 472 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) = 80 |
Polycyclic presentation:
2^6,5^2|a^2=d,c^2=f,b^a=bf,c^a=cf,g^a=g^2,h^a=h^2,c^b=ce,g^b=g^4,g^d=g^4,h^d=h^464 conjugacy classes — view the full character table.
| maximal subgroup of | #72221534, #72221538, #72221541, … |
| maximal normal subgroup of | #72221534, #72221538, #72221541, … |
| maximal quotient of | #72221301, #72221302, #72223348, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 6342);