Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C52 ⋊ #100 |
112 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
Polycyclic presentation:
2^5,5^2|b^2=c,c^2=e,b^a=bd,c^a=ce,g^a=g^4,d^b=de,f^b=f^483 conjugacy classes — view the full character table.
| maximal subgroup of | #13100576, #13100577, #13101099, … |
| maximal normal subgroup of | #13100576, #13100577, #13101099, … |
| maximal quotient of | #13099256, #13099260, #13099265, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 258);