Finite Group DatabasebetaFinite Group Databasebeta| order | 1696 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | C2×C22⋊#6157 |
| unambiguous semidirect product | D53⋊(C22⋊C4) |
| unambiguous semidirect product | (C2×#6157)⋊C22 |
| Fitting | C23×C53 ⋊ C4 |
| Sylow | C53 ⋊ C2×C22⋊C4 |
132 conjugacy classes of subgroups.
| transitive degree | μt(G) = 424 |
124 conjugacy classes — view the full character table.
| maximal subgroup of | #16811500, #16811501, C4×C22⋊#6157, … |
| maximal normal subgroup of | #16811500, #16811501, C4×C22⋊#6157, … |
| maximal quotient of | C2×(C2×#6157)⋊C4, C4×C22⋊#6157, #16811564, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1696, 223);