Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×C52×D4 ⋊ C22 |
| Sylow | C52 ⋊ #576 |
604 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
Polycyclic presentation:
2^6,5^2|e^2=f,c^a=cf,g^a=g^4,d^b=de,e^b=ef,h^b=h^4,e^d=ef124 conjugacy classes — view the full character table.
| maximal subgroup of | #72220868, #72221385, #72221388, … |
| maximal normal subgroup of | #72220868, #72221385, #72221388, … |
| maximal quotient of | #72242550 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 8637);