Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| isoclinism | isoclinic class of Dic50 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×C4⋊Dic25 |
| Sylow | C25 ⋊ C2×C4⋊C4 |
138 conjugacy classes of subgroups.
| transitive degree | μt(G) = 800 |
212 conjugacy classes — view the full character table.
| maximal subgroup of | #13097736, #13097758, #13097763, … |
| maximal normal subgroup of | #13097736, #13097758, #13097763, … |
| maximal quotient of | C2×C4⋊#6014, #13098199, C4×C4⋊Dic25, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 146);