Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| isoclinism | isoclinic class of #686 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C2 |
| direct product | C5×#3942 |
| Sylow | C52 ⋊ #103 |
110 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
170 conjugacy classes — view the full character table.
| maximal subgroup of | #13100618, #13100620, #13100622, … |
| maximal normal subgroup of | #13100618, #13100620, #13100622, … |
| maximal quotient of | C5×#64672, C5×#64704, C5×#64706, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 295);