Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22×C5 |
No aliases for this group.
| Fitting | C2×C52×Q8 ⋊ C2 |
| Sylow | C52 ⋊ #137 |
240 conjugacy classes of subgroups.
| transitive degree | μt(G) = 400 |
Polycyclic presentation:
2^5,5^2|b^2=e,c^2=e,d^2=e,c^a=cd,d^a=de,f^a=f^4,g^a=g^4,c^b=ce,d^c=de131 conjugacy classes — view the full character table.
| maximal subgroup of | #13101810, #13101811, #13101840, … |
| maximal normal subgroup of | #13101810, #13101811, #13101840, … |
| maximal quotient of | #13102826, #13102828, #13102848, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 921);