Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C52 ⋊ #453 |
444 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 64 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 40 |
Polycyclic presentation:
2^6,5^2|b^2=ef,e^2=f,b^a=be,d^a=df,e^a=ef,g^a=g^4,c^b=cd,d^b=df,h^b=h^4,e^c=ef112 conjugacy classes — view the full character table.
| maximal subgroup of | #72213351, C2×#13101698, #72223049, … |
| maximal normal subgroup of | #72213351, C2×#13101698, #72223049, … |
| maximal quotient of | C2×#13101698, #72223341 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 4050);