Finite Group DatabasebetaFinite Group Databasebeta| order | 1696 |
| isoclinism | isoclinic class of #6157 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C23×#6157 |
| unambiguous semidirect product | D53⋊(C22×C4) |
| Fitting, socle | C23×C53 ⋊ C4 |
| derived, Sylow | C53 ⋊ C23×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | #6157 |
| commutator, hypocenter | C53 | C23×C4 |
| Frattini | C1 | G |
| Fitting, socle | C23×C53 | C4 |
| prime radical | C23×D53 | C2 |
| cosocle | D53 | C24 |
| LCS | G ▷ C53 | |
| UCS | C1 ◁ C23 | |
236 conjugacy classes of subgroups.
| transitive degree | μt(G) = 424 |
136 conjugacy classes — view the full character table.
| maximal subgroup of | C2×(C2×#6157)⋊C4, C22⋊C4×#6157, #16811570, … |
| maximal normal subgroup of | C2×(C2×#6157)⋊C4, C22⋊C4×#6157, #16811570, … |
| maximal quotient of | C22×C4×#6157, C22×C22⋊#6157, C22×C4⋊#6157, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1696, 235);