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 38 normal subgroups are shown.
This group has 140 conjugacy classes of subgroups — too many to draw. Only its 38 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,c^2=d,d^2=e,c^a=cd,d^a=de,g^a=g^4,c^b=cde,d^b=de,f^b=f^471 conjugacy classes — view the full character table.
| maximal subgroup of | #13105776, #13105777, C2×#11716929, … |
| maximal normal subgroup of | #13105776, #13105777, C2×#11716929, … |
| maximal quotient of | #13100852, #13100853, #13100877, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 588);