Finite Group DatabasebetaFinite Group Databasebeta| order | 1232 |
| isoclinism | isoclinic class of D11 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7×C8 · Schur multiplier (H2) = C2 |
| direct product | C2×C7×C11⋊C8 |
| unambiguous semidirect product | (C2×C11)⋊(C7×C8) |
| derived, Sylow | C11 ⋊ C2×C7×C8 |
| Hall | C7×C11 ⋊ C2×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4×C7 | D11 |
| commutator, hypocenter | C11 | C2×C7×C8 |
| Frattini | C4 | C2×C7×D11 |
| Fitting | C2×C4×C7×C11 | C2 |
| socle, prime radical | C22×C7×C11 | C4 |
| cosocle | C4×C11 | C22×C7 |
| LCS | G ▷ C11 | |
| UCS | C1 ◁ C2×C4×C7 | |
44 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1232 |
392 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1232, 35);