Finite Group DatabasebetaFinite Group Databasebeta| order | 1696 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×Q8×D53 |
| Fitting | C2×Q8×C53 ⋊ C2 |
| Sylow | C53 ⋊ C22×Q8 |
156 conjugacy classes of subgroups.
| transitive degree | μt(G) = 848 |
280 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #101×D53, #103×D53, #16810630, … |
| maximal normal subgroup of | #101×D53, #103×D53, #16810630, … |
| maximal quotient of | C2×C4⋊C4×D53, C4×Q8×D53, C2×#13133182, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1696, 185);