Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×D4×C25 ⋊ C2 |
| Sylow | C25 ⋊ AGL(1,ℤ/8) |
102 conjugacy classes of subgroups.
| transitive degree | μt(G) = 200 |
Polycyclic presentation:
2^5,5^2|b^2=e,d^2=e,f^5=g,c^a=cd,d^a=de,f^a=f^4g^4,g^a=g^4,c^b=ce,d^c=de131 conjugacy classes — view the full character table.
| maximal subgroup of | #13098023, #13098024, #13098337, … |
| maximal normal subgroup of | #13098023, #13098024, #13098337, … |
| maximal quotient of | #13098238, #13098240, #13098244, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 154);