Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2×C5 |
No aliases for this group.
| Sylow | C52 ⋊ #107 |
73 conjugacy classes of subgroups.
| transitive degree | μt(G) = 40 |
Polycyclic presentation:
2^5,5^2|a^2=c,b^2=cd,c^2=e,d^2=e,b^a=bc,f^a=f^2,g^a=g^3,c^b=ce,d^b=de,f^b=g,g^b=f^4,f^c=f^4,g^c=g^426 conjugacy classes — view the full character table.
| maximal subgroup of | #13103312, #13103314, #13103315, … |
| maximal normal subgroup of | #13103312, #13103314, #13103315, … |
| maximal quotient of | #13100017, #13100018, #13100019, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 463);