Finite Group DatabasebetaFinite Group Databasebeta| order | 1696 |
| isoclinism | isoclinic class of Dic106 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C4×C22⋊D53 |
| Fitting | C22×C4×C53 ⋊ C2 |
| Sylow | C53 ⋊ C4×D4 |
94 conjugacy classes of subgroups.
| transitive degree | μt(G) = 848 |
436 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #16810686, C8×C22⋊D53, #16810691, … |
| maximal normal subgroup of | #16810686, C8×C22⋊D53, #16810691, … |
| maximal quotient of | C4×C22⋊Dic53, C4×#11719921, C4×#11719919, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1696, 107);