Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C52 ⋊ #322 |
264 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1600 |
Polycyclic presentation:
2^6,5^2|a^2=c,b^2=d,c^2=f,d^2=e,b^a=be,g^a=g^2,h^a=h^2,g^c=g^4,h^c=h^4136 conjugacy classes — view the full character table.
| maximal subgroup of | #72220897, #72221170, #72221172, … |
| maximal normal subgroup of | #72220897, #72221170, #72221172, … |
| maximal quotient of | #72242130, #72242134 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 2610);