Finite Group DatabasebetaFinite Group Databasebeta| order | 816 |
| isoclinism | isoclinic class of D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8×C17 · Schur multiplier (H2) = C2 |
| direct product | D3×C8×C17 |
| Fitting | C3×C8×C17 ⋊ C2 |
| derived, Sylow | C3 ⋊ C2×C8×C17 |
| Hall | C3×C17 ⋊ C2×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C8×C17 | D3 |
| commutator, hypocenter | C3 | C2×C8×C17 |
| Frattini | C4 | C2×D3×C17 |
| Fitting | C3×C8×C17 | C2 |
| socle | C2×C3×C17 | C2×C4 |
| prime radical | C2×D3×C17 | C4 |
| cosocle | C3×C4 | C22×C17 |
| LCS | G ▷ C3 | |
| UCS | C1 ◁ C8×C17 | |
44 conjugacy classes of subgroups.
| transitive degree | μt(G) = 408 |
408 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×#63214, #13108676, D3×C16×C17, … |
| maximal normal subgroup of | D3×#63214, #13108676, D3×C16×C17, … |
| maximal quotient of | D3×C16×C17, C17×#798, C8×Dic3×C17, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(816, 49);