Finite Group DatabasebetaFinite Group Databasebeta| order | 816 |
| isoclinism | isoclinic class of D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C16×C17 · Schur multiplier (H2) = C1 |
| direct product | C17×C3⋊C16 |
| unambiguous semidirect product | C3⋊(C16×C17) |
| derived, Sylow | C3 ⋊ C16×C17 |
| Hall | C3×C17 ⋊ C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C8×C17 | D3 |
| commutator, hypocenter | C3 | C16×C17 |
| Frattini | C8 | D3×C17 |
| Fitting | C3×C8×C17 | C2 |
| socle, prime radical | C2×C3×C17 | C8 |
| cosocle | C3×C8 | C2×C17 |
| LCS | G ▷ C3 | |
| UCS | C1 ◁ C8×C17 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 816 |
408 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D17×C3⋊C16, #13108674, #13108675, … |
| maximal normal subgroup of | D17×C3⋊C16, #13108674, #13108675, … |
| maximal quotient of | C17×C3⋊C32, C2×C17×C3⋊C16 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(816, 1);