Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C42 |
No aliases for this group.
| Fitting | C42×C52 ⋊ C4 |
| Sylow | C52 ⋊ #376 |
712 conjugacy classes of subgroups.
| transitive degree | μt(G) = 400 |
Polycyclic presentation:
2^6,5^2|a^2=d,b^2=f,c^2=e,c^a=cf,g^a=g^2,h^a=h^2,g^d=g^4,h^d=h^4136 conjugacy classes — view the full character table.
| maximal subgroup of | #117×#1043, C4×#11717438, #72221153, … |
| maximal normal subgroup of | #117×#1043, C4×#11717438, #72221153, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 7050);