Finite Group DatabasebetaFinite Group Databasebeta| order | 1232 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Hall | C7×C11 ⋊ Q16 |
| Sylow | C11 ⋊ Dic28 |
| Sylow | C7 ⋊ #4326 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | #10597507 |
| commutator, Fitting, cosocle | C4×C7×C11 | C22 |
| Frattini, hypercenter | C4 | D7×D11 |
| socle, prime radical | C2×C7×C11 | D4 |
| hypocenter | C7×C11 | Q16 |
| LCS | G ▷ C4×C7×C11 ▷ C2×C7×C11 ▷ C7×C11 | |
| UCS | C1 ◁ C2 ◁ C4 | |
36 conjugacy classes of subgroups.
| minimal degree | μ(G) = 34 |
| transitive degree | μt(G) = 1232 |
Polycyclic presentation:
2^4,7,11|a^2=c,b^2=d,c^2=d,b^a=bc,f^a=f^10,c^b=cd,e^b=e^6116 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1232, 22);