Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C52×C16 ⋊ C4 |
| Sylow | C52 ⋊ #366 |
184 conjugacy classes of subgroups.
| transitive degree | μt(G) = 400 |
Polycyclic presentation:
2^6,5^2|a^2=c,b^2=de,d^2=ef,e^2=f,b^a=bd,d^a=de,e^a=ef,g^a=g^2,h^a=h^2,g^c=g^4,h^c=h^4118 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#13100228, #72242311, D16×#1043, … |
| maximal normal subgroup of | C2×#13100228, #72242311, D16×#1043, … |
| maximal quotient of | C2×#13100228, #72242307 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 2580);