Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25×C5 |
| direct product | C2×Q8×C5⋊D5 |
| Fitting | C2×C52×Q8 ⋊ C2 |
| Sylow | C52 ⋊ C22×Q8 |
624 conjugacy classes of subgroups.
| transitive degree | μt(G) = 400 |
140 conjugacy classes — view the full character table.
| maximal subgroup of | #13101721, #13101729, #13101758, … |
| maximal normal subgroup of | #13101721, #13101729, #13101758, … |
| maximal quotient of | C2×#11717207, C2×#11717216, C2×#11717208, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 1177);