Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C52 ⋊ #347 |
107 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
Polycyclic presentation:
2^6,5^2|a^2=d,b^2=c,c^2=e,d^2=f,e^2=f,b^a=be,c^a=cf,h^a=h^4,d^b=df,g^b=g^2,g^c=g^494 conjugacy classes — view the full character table.
| maximal subgroup of | #72220674 |
| maximal normal subgroup of | #72220674 |
| maximal quotient of | #72242277, #72242284 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 2159);