Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C52 ⋊ #104 |
94 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^5,5^2|a^2=c,d^2=e,b^a=bd,g^a=g^2,c^b=ce,d^b=de,f^b=f^4,g^c=g^459 conjugacy classes — view the full character table.
| maximal subgroup of | #13103459, #13103460, #13103461, … |
| maximal normal subgroup of | #13103459, #13103460, #13103461, … |
| maximal quotient of | #13099751, #13099757, #13099758, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 398);