Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C4×C5 |
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=d,b^2=c,c^2=e,d^2=f,b^a=be,g^a=g^4,h^a=h^4424 conjugacy classes — view the full character table.
| maximal subgroup of | C5⋊D5×#322, #72221022, #72221084, … |
| maximal normal subgroup of | C5⋊D5×#322, #72221022, #72221084, … |
| maximal quotient of | #72242120 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 1841);