Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23×C5 |
No aliases for this group.
| Sylow | C52 ⋊ #442 |
528 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 189 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 800 |
Polycyclic presentation:
2^6,5^2|a^2=e,d^2=f,c^a=cf,g^a=g^4,h^a=h^4,c^b=cd,d^b=df,d^c=df190 conjugacy classes — view the full character table.
| maximal subgroup of | C5⋊D5×#442, #72220754, #72223075, … |
| maximal normal subgroup of | C5⋊D5×#442, #72220754, #72223075, … |
| maximal quotient of | C2×#13103012, #72253069, #72253107 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 5364);