Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C52 ⋊ #102 |
154 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 154 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|a^2=c,b^2=cde,d^2=e,b^a=bd,d^a=de,g^a=g^4,f^b=f^498 conjugacy classes — view the full character table.
| maximal subgroup of | #13100459, #13100460, #13100471, … |
| maximal normal subgroup of | #13100459, #13100460, #13100471, … |
| maximal quotient of | #13099252, #13099261, #13099263, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 264);