Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C52 ⋊ #568 |
584 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
Polycyclic presentation:
2^6,5^2|b^2=e,e^2=f,d^a=df,g^a=g^4,c^b=cf,h^b=h^4178 conjugacy classes — view the full character table.
| maximal subgroup of | #72220837, #72221383, #72221388, … |
| maximal normal subgroup of | #72220837, #72221383, #72221388, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 8257);