Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4×C5 |
No aliases for this group.
| Fitting | C2×C52×D4 ⋊ C4 |
| Sylow | C52 ⋊ #410 |
480 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 66 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,b^2=f,c^a=ce,e^a=ef,g^a=g^3,h^a=h^2,c^b=cf,d^c=df,g^d=g^4,h^d=h^482 conjugacy classes — view the full character table.
| maximal subgroup of | #72221127, #72226449, #72226489, … |
| maximal normal subgroup of | #72221127, #72226449, #72226489, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 7259);