Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| isoclinism | isoclinic class of #677 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C22 |
| direct product | C5×#3953 |
| Fitting | C2×C52×C8 ⋊ C2 |
| Sylow | C52 ⋊ #102 |
122 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
230 conjugacy classes — view the full character table.
| maximal subgroup of | #13100846, #13100907, #13100912, … |
| maximal normal subgroup of | #13100846, #13100907, #13100912, … |
| maximal quotient of | C5×#64679, C5×#64690, C5×#64705, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 306);