Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×C4×C52 ⋊ C2×C4 |
| Sylow | C52 ⋊ #386 |
599 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 599 conjugacy classes of subgroups — too many to draw. Only its 94 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^6,5^2|a^2=d,c^2=e,c^a=cf,g^a=g^2,c^b=ce,h^b=h^4,g^d=g^494 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#65779 |
| maximal normal subgroup of | D5×#65779 |
| maximal quotient of | #72221596, #72221615, #72221693, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 6065);