Finite Group DatabasebetaFinite Group Databasebeta| order | 1696 |
| isoclinism | isoclinic class of D53 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
| direct product | C2×#11719908 |
| derived, Sylow | C53 ⋊ C2×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C8 | D53 |
| commutator, hypocenter | C53 | C2×C16 |
| Frattini | C8 | C2×D53 |
| Fitting | C2×C8×C53 | C2 |
| socle, prime radical | C22×C53 | C8 |
| cosocle | C8×C53 | C22 |
| LCS | G ▷ C53 | |
| UCS | C1 ◁ C2×C8 | |
28 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1696 |
448 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C16×Dic53, C4×#11719908, #16810398, … |
| maximal normal subgroup of | C16×Dic53, C4×#11719908, #16810398, … |
| maximal quotient of | C4×#11719908, C22⋊#11719908, C4⋊#11719908, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1696, 84);