Finite Group DatabasebetaFinite Group Databasebeta| order | 792 |
| isoclinism | isoclinic class of #157 |
| automorphism | ? |
| homology | Abelianization (H1) = C8×C11 · Schur multiplier (H2) = C3 |
| direct product | C11×#622 |
| derived, Sylow | C32 ⋊ C8×C11 |
| Hall | C32×C11 ⋊ C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C11 | #157 |
| commutator, hypocenter | C32 | C8×C11 |
| Frattini | C2 | C11×#157 |
| Fitting, socle, prime radical | C2×C32×C11 | C4 |
| cosocle | C3⋊Dic3 | C2×C11 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C2×C11 | |
28 conjugacy classes of subgroups.
| transitive degree | μt(G) = 264 |
132 conjugacy classes — view the full character table.
| maximal subgroup of | C11×#3771, C11⋊#3771, D11×#622, … |
| maximal normal subgroup of | C11×#3771, C11⋊#3771, D11×#622, … |
| maximal quotient of | C11×#3708, C2×C11×#622 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(792, 46);