Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23×C5 |
No aliases for this group.
| Fitting | C52×AGL(1,ℤ/8) ⋊ C2 |
| Sylow | C52 ⋊ #453 |
672 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 672 conjugacy classes of subgroups — too many to draw. Only its 111 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 200 |
Polycyclic presentation:
2^6,5^2|d^2=f,e^2=f,c^a=ce,e^a=ef,g^a=g^4,h^a=h^4,c^b=cd,d^b=df,d^c=df,e^c=ef148 conjugacy classes — view the full character table.
| maximal subgroup of | C5⋊D5×#453, C2×#13103063, #72223380, … |
| maximal normal subgroup of | C5⋊D5×#453, C2×#13103063, #72223380, … |
| maximal quotient of | C2×#13103063 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 5415);