Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| unambiguous semidirect product | D5⋊#3966 |
| Fitting | C2×C52×D4 ⋊ C4 |
| Sylow | C52 ⋊ C2×#99 |
447 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 447 conjugacy classes of subgroups — too many to draw. Only its 89 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^a=ce,e^a=ef,g^a=g^2,h^a=h^4,c^b=cf,d^c=df,g^d=g^4112 conjugacy classes — view the full character table.
| maximal subgroup of | D5×D5⋊#99, #72221749, #72221750, … |
| maximal normal subgroup of | D5×D5⋊#99, #72221749, #72221750, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 7006);