Finite Group DatabasebetaFinite Group Databasebeta| order | 816 |
| isoclinism | isoclinic class of D3×D17 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| direct product | C3⋊C8×D17 |
| derived, Hall | C3×C17 ⋊ C2×C8 |
| Sylow | C17 ⋊ C2×C3⋊C8 |
| Sylow | C3 ⋊ C8×D17 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C4 | D3×D17 |
| commutator, hypocenter | C3×C17 | C2×C8 |
| Fitting, cosocle | C3×C4×C17 | C22 |
| socle | C2×C3×C17 | C2×C4 |
| prime radical | C2×C3×D17 | C4 |
| LCS | G ▷ C3×C17 | |
| UCS | C1 ◁ C4 | |
44 conjugacy classes of subgroups.
| transitive degree | μt(G) = 408 |
120 conjugacy classes — view the full character table.
| maximal subgroup of | C3⋊C8×#595, #13108885, #13108886, … |
| maximal normal subgroup of | C3⋊C8×#595, #13108885, #13108886, … |
| maximal quotient of | D17×C3⋊C16, #13108675, C3⋊C8×Dic17, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(816, 7);