Finite Group DatabasebetaFinite Group Databasebeta| order | 792 |
| isoclinism | isoclinic class of D32⋊D11 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D32⋊D11 |
| Fitting, socle, Hall | C32×C11 ⋊ D4 |
| Sylow | C11 ⋊ GO+(4,𝔽2) |
| Sylow | C32 ⋊ C22⋊D11 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle | C11×C3⋊D3 | C22 |
| Fitting, socle, hypocenter | C32×C11 | D4 |
| LCS | G ▷ C11×C3⋊D3 ▷ C32×C11 | |
| UCS | C1 | |
52 conjugacy classes of subgroups.
| transitive degree | μt(G) = 66 |
Polycyclic presentation:
2^3,3^2,11|b^a=bc,d^a=d^2,e^a=d^2e,f^a=f^10,d^b=d^2e^2,d^c=d^2,e^c=e^254 conjugacy classes — view the full character table.
| maximal subgroup of | D11×GO+(4,𝔽2), C2×D32⋊D11, #72259148 |
| maximal normal subgroup of | D11×GO+(4,𝔽2), C2×D32⋊D11, #72259148 |
| maximal quotient of | #13097225, D32⋊Dic11, #13097227, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(792, 112);