Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C4⋊C4×C25 ⋊ C4 |
| Sylow | C25 ⋊ #327 |
135 conjugacy classes of subgroups; only the 31 normal subgroups are shown.
This group has 135 conjugacy classes of subgroups — too many to draw. Only its 31 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 400 |
Polycyclic presentation:
2^6,5^2|a^2=c,b^2=f,d^2=ef,g^5=h,b^a=bd,d^a=de,g^a=g^2h,h^a=h^2,c^b=cf,d^b=def,g^c=g^4h^4,h^c=h^479 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 210);