Finite Group DatabasebetaFinite Group Databasebeta| order | 704 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
| direct product | D11×#125 |
| Fitting | C11×#125 ⋊ C2 |
| Sylow | C11 ⋊ C2×#125 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D11 |
| commutator, socle, cosocle | C22×C11 | C24 |
| Fitting | C11×#125 | C2 |
| prime radical | C22×D11 | C23 |
| hypercenter | #125 | D11 |
| hypocenter | C11 | C2×#125 |
| LCS | G ▷ C22×C11 ▷ C11 | |
| UCS | C1 ◁ C22 ◁ #125 | |
226 conjugacy classes of subgroups.
| transitive degree | μt(G) = 352 |
98 conjugacy classes — view the full character table.
| maximal subgroup of | D11×#330, #13067216, #13067241, … |
| maximal normal subgroup of | D11×#330, #13067216, #13067241, … |
| maximal quotient of | D11×#382, D11×#387, D11×#389, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(704, 1137);