Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C4⋊C4×D25 |
| Fitting | C4⋊C4×C25 ⋊ C2 |
| Sylow | C25 ⋊ C2×C4⋊C4 |
138 conjugacy classes of subgroups.
| transitive degree | μt(G) = 400 |
140 conjugacy classes — view the full character table.
| maximal subgroup of | #13097861, #102×D25, #13098047, … |
| maximal normal subgroup of | #13097861, #102×D25, #13098047, … |
| maximal quotient of | #13097922, #13097925, #13097926, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 112);