Finite Group DatabasebetaFinite Group Databasebeta| order | 1696 |
| isoclinism | isoclinic class of Dic106 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C22×Dic106 |
| Sylow | C53 ⋊ C22×Q8 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C2×D53 |
| commutator, cosocle | C2×C53 | C24 |
| Frattini | C2 | C23×D53 |
| Fitting | C22×C4×C53 | C2 |
| socle, prime radical | C23×C53 | C22 |
| hypercenter | C22×C4 | D53 |
| hypocenter | C53 | C22×Q8 |
| LCS | G ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C23 ◁ C22×C4 | |
156 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1696 |
436 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #16810527, #16810528, #16810529, … |
| maximal normal subgroup of | #16810527, #16810528, #16810529, … |
| maximal quotient of | C22×#11719919, C22×C4⋊Dic53, C2×C4×Dic106, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1696, 186);