Finite Group DatabasebetaFinite Group Databasebeta| order | 1696 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C2×D4×D53 |
| Fitting | C2×D4×C53 ⋊ C2 |
| Sylow | C53 ⋊ C22×D4 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22×D53 |
| commutator, cosocle | C2×C53 | C24 |
| Frattini | C2 | C23×D53 |
| Fitting | C2×D4×C53 | C2 |
| socle | C22×C53 | C23 |
| hypercenter | C2×D4 | D53 |
| hypocenter | C53 | C22×D4 |
| LCS | G ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C22 ◁ C2×D4 | |
236 conjugacy classes of subgroups.
| transitive degree | μt(G) = 424 |
280 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #99×D53, #100×D53, #102×D53, … |
| maximal normal subgroup of | #99×D53, #100×D53, #102×D53, … |
| maximal quotient of | C2×C22⋊C4×D53, C2×C4⋊C4×D53, C4×D4×D53, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1696, 182);