Finite Group DatabasebetaFinite Group Databasebeta| order | 704 |
| isoclinism | isoclinic class of #4314 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C22×D88 |
| Fitting | C22×C8×C11 ⋊ C2 |
| Sylow | C11 ⋊ C22×D8 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | D44 |
| commutator, cosocle | C4×C11 | C24 |
| Frattini | C4 | C23×D11 |
| Fitting | C22×C8×C11 | C2 |
| socle | C23×C11 | D4 |
| hypercenter | C22×C8 | D11 |
| hypocenter | C11 | C22×D8 |
| LCS | G ▷ C4×C11 ▷ C2×C11 ▷ C11 | |
| UCS | C1 ◁ C23 ◁ C22×C4 ◁ C22×C8 | |
338 conjugacy classes of subgroups.
| transitive degree | μt(G) = 352 |
188 conjugacy classes — view the full character table.
| maximal subgroup of | #13068963, #13068965, #13069480, … |
| maximal normal subgroup of | #13068963, #13068965, #13069480, … |
| maximal quotient of | C22×#66885, C22×#66882, C2×C4×D88, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(704, 1190);