Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C52 ⋊ C4×C4⋊C4 |
496 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 101 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 80 |
Polycyclic presentation:
2^6,5^2|a^2=d,b^2=f,c^2=e,g^a=g^2,h^a=h^2,c^b=cf,g^b=g^4,g^d=g^4,h^d=h^476 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#11717375, #72221487, #72221534, … |
| maximal normal subgroup of | C4×#11717375, #72221487, #72221534, … |
| maximal quotient of | #72220745, #72220761, #72221293, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 6326);