Finite Group DatabasebetaFinite Group Databasebeta| order | 1232 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | (C2×D11)⋊Dic7 |
| Hall | C7×C11 ⋊ C22⋊C4 |
| Sylow | C11 ⋊ C22⋊Dic7 |
| Sylow | C7 ⋊ (C2×D11)⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C22 | D7×D11 |
| commutator | C2×C7×C11 | C2×C4 |
| Fitting, socle, cosocle | C22×C7×C11 | C22 |
| prime radical | C22×C7×D11 | C2 |
| hypocenter | C7×C11 | C22⋊C4 |
| LCS | G ▷ C2×C7×C11 ▷ C7×C11 | |
| UCS | C1 ◁ C22 | |
68 conjugacy classes of subgroups.
| transitive degree | μt(G) = 616 |
Polycyclic presentation:
2^4,7,11|b^2=c,b^a=bd,f^a=f^10,e^b=e^6134 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1232, 24);