Finite Group DatabasebetaFinite Group Databasebeta| order | 1696 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C4⋊C4×D53 |
| Fitting | C4⋊C4×C53 ⋊ C2 |
| Sylow | C53 ⋊ C2×C4⋊C4 |
92 conjugacy classes of subgroups.
| transitive degree | μt(G) = 848 |
280 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #102×D53, #103×D53, #16810621, … |
| maximal normal subgroup of | #102×D53, #103×D53, #16810621, … |
| maximal quotient of | #95×D53, #16810474, C4⋊C4×Dic53, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1696, 99);