Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | D5⋊#4010 |
| Fitting | C52×Q8 ⋊ C2×C4 |
| Sylow | C52 ⋊ C2×#104 |
384 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 384 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) = 80 |
Polycyclic presentation:
2^6,5^2|a^2=d,c^2=f,e^2=f,c^a=ce,g^a=g^2,h^a=h^2,c^b=cf,g^b=g^4,d^c=df,e^c=ef,g^d=g^4,h^d=h^458 conjugacy classes — view the full character table.
| maximal subgroup of | #72221790 |
| maximal normal subgroup of | #72221790 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 6421);