Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4×C5 |
No aliases for this group.
| Fitting | C2×C52×D8 ⋊ C2 |
| Sylow | C52 ⋊ #496 |
576 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 576 conjugacy classes of subgroups — too many to draw. Only its 127 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 800 |
Polycyclic presentation:
2^6,5^2|a^2=e,d^2=f,b^a=be,c^a=cef,g^a=g^4,h^a=h^4,c^b=cd,d^b=df,d^c=df184 conjugacy classes — view the full character table.
| maximal subgroup of | C5⋊D5×#496, #72220962, #72220976, … |
| maximal normal subgroup of | C5⋊D5×#496, #72220962, #72220976, … |
| maximal quotient of | #72223024, #72223034, #72223044, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 5366);