Finite Group DatabasebetaFinite Group Databasebeta| order | 1696 |
| isoclinism | isoclinic class of #6157 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
| direct product | C2×#11719910 |
| derived, Sylow | C53 ⋊ C2×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | #6157 |
| commutator, hypocenter | C53 | C2×C16 |
| Frattini | C4 | C2×#6157 |
| Fitting | C2×C4×C53 | C4 |
| socle, prime radical | C22×C53 | C8 |
| cosocle | #88322 | C22 |
| LCS | G ▷ C53 | |
| UCS | C1 ◁ C2×C4 | |
28 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1696 |
136 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#11719910, #16811509, #16811511, … |
| maximal normal subgroup of | C4×#11719910, #16811509, #16811511, … |
| maximal quotient of | C4×#11719910, C22⋊#11719910, C4⋊#11719910, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1696, 218);