Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C52 ⋊ C2×Q32 |
224 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 46 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^6,5^2|a^2=f,b^2=f,c^2=f,d^2=ef,e^2=f,c^a=cd,d^a=de,e^a=ef,g^a=g^4,c^b=cd,d^b=de,e^b=ef,h^b=h^4,d^c=de,e^c=ef94 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 3576);