Finite Group DatabasebetaFinite Group Databasebeta| order | 792 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Hall | C32×C11 ⋊ Q8 |
| Sylow | C11 ⋊ #634 |
| Sylow | C32 ⋊ Dic22 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C3⋊D3×D11 |
| commutator, Fitting, socle, prime radical, cosocle | C2×C32×C11 | C22 |
| hypocenter | C32×C11 | Q8 |
| LCS | G ▷ C2×C32×C11 ▷ C32×C11 | |
| UCS | C1 ◁ C2 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 792 |
Polycyclic presentation:
2^3,3^2,11|a^2=c,b^2=c,b^a=bc,f^a=f^10,d^b=d^2,e^b=e^281 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#63143, #13097260, #13097272, … |
| maximal normal subgroup of | D3×#63143, #13097260, #13097272, … |
| maximal quotient of | Dic11⋊(C3⋊Dic3), #13097052, #13097053, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(792, 61);