Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×C8×C25 ⋊ C2 |
| Sylow | C25 ⋊ C22⋊C8 |
75 conjugacy classes of subgroups.
| transitive degree | μt(G) = 400 |
Polycyclic presentation:
2^5,5^2|b^2=c,c^2=e,f^5=g,b^a=bd,f^a=f^4g^4,g^a=g^4212 conjugacy classes — view the full character table.
| maximal subgroup of | #13097962, C8×D100, #13097965, … |
| maximal normal subgroup of | #13097962, C8×D100, #13097965, … |
| maximal quotient of | #13097668, #13097669, #13097673, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 27);