Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C52 ⋊ #137 |
140 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 140 conjugacy classes of subgroups — too many to draw. Only its 40 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:
2^5,5^2|b^2=e,d^2=e,c^a=ce,g^a=g^4,c^b=cd,d^b=de,f^b=f^4,d^c=de65 conjugacy classes — view the full character table.
| maximal subgroup of | #13105819, #13105820, #13105827, … |
| maximal normal subgroup of | #13105819, #13105820, #13105827, … |
| maximal quotient of | #13100593, #13100622, #13100623, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 706);