Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C52×#41 ⋊ C4 |
| Sylow | C52 ⋊ #416 |
632 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 632 conjugacy classes of subgroups — too many to draw. Only its 104 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 400 |
Polycyclic presentation:
2^6,5^2|a^2=d,b^2=f,e^2=f,c^a=ce,e^a=ef,g^a=g^2,h^a=h^2,e^c=ef,g^d=g^4,h^d=h^488 conjugacy classes — view the full character table.
| maximal subgroup of | #135×#1043, #72253172, #72253176, … |
| maximal normal subgroup of | #135×#1043, #72253172, #72253176, … |
| maximal quotient of | C4×#11716875, C2×#13104807 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 7159);