Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C52 ⋊ C2×#97 |
584 conjugacy classes of subgroups.
| transitive degree | μt(G) = 800 |
Polycyclic presentation:
2^6,5^2|a^2=d,b^2=f,c^2=e,d^2=f,c^a=cf,g^a=g^2,h^a=h^2,g^d=g^4,h^d=h^4136 conjugacy classes — view the full character table.
| maximal subgroup of | #97×#1043, #72220732, #72220803, … |
| maximal normal subgroup of | #97×#1043, #72220732, #72220803, … |
| maximal quotient of | #72221171, #72242145, C2×#13104688 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 7040);