Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4×C5 |
No aliases for this group.
| Sylow | C52 ⋊ #492 |
568 conjugacy classes of subgroups.
| transitive degree | μt(G) = 800 |
Polycyclic presentation:
2^6,5^2|a^2=e,e^2=f,b^a=bef,c^a=cef,g^a=g^4,h^a=h^4,c^b=cd,e^b=ef,e^c=ef190 conjugacy classes — view the full character table.
| maximal subgroup of | C5⋊D5×#492, #72220958, #72220976, … |
| maximal normal subgroup of | C5⋊D5×#492, #72220958, #72220976, … |
| maximal quotient of | #72221135, #72223034 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 5289);