Finite Group DatabasebetaFinite Group Databasebeta| order | 704 |
| isoclinism | isoclinic class of D11 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4 |
| direct product | C22×C4×Dic11 |
| derived, Sylow | C11 ⋊ C22×C42 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23×C4 | D11 |
| commutator, hypocenter | C11 | C22×C42 |
| Frattini | C22 | C23×D11 |
| Fitting | C23×C4×C11 | C2 |
| socle, prime radical | C24×C11 | C22 |
| cosocle | C22×C11 | C24 |
| LCS | G ▷ C11 | |
| UCS | C1 ◁ C23×C4 | |
498 conjugacy classes of subgroups.
| transitive degree | μt(G) = 704 |
224 conjugacy classes — view the full character table.
| maximal subgroup of | #95×Dic11, C4×C11⋊#95, #13066840, … |
| maximal normal subgroup of | #95×Dic11, C4×C11⋊#95, #13066840, … |
| maximal quotient of | C2×C42×Dic11, C22×C11⋊#95, C2×#10622545, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(704, 1232);