Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C52 ⋊ #417 |
416 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 65 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 40 |
Polycyclic presentation:
2^6,5^2|a^2=d,e^2=f,b^a=be,e^a=ef,g^a=g^2,h^a=h^2,c^b=cf,e^b=ef,g^b=g^4,g^d=g^4,h^d=h^458 conjugacy classes — view the full character table.
| maximal subgroup of | #72213282, #72213383, #72213446, … |
| maximal normal subgroup of | #72213282, #72213383, #72213446, … |
| maximal quotient of | #72220789, C2×#13103931, #72221082, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 6283);