Finite Group DatabasebetaFinite Group Databasebeta| order | 816 |
| isoclinism | isoclinic class of D3×D17 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×Dic3×D17 |
| derived, Hall | C3×C17 ⋊ C22×C4 |
| Sylow | C17 ⋊ C22×Dic3 |
| Sylow | C3 ⋊ C2×C4×D17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | D3×D17 |
| commutator, hypocenter | C3×C17 | C22×C4 |
| Frattini | C2 | C2×D3×D17 |
| Fitting, socle | C22×C3×C17 | C22 |
| prime radical | C22×C3×D17 | C2 |
| cosocle | C2×C3×C17 | C23 |
| LCS | G ▷ C3×C17 | |
| UCS | C1 ◁ C22 | |
108 conjugacy classes of subgroups.
| transitive degree | μt(G) = 408 |
120 conjugacy classes — view the full character table.
| maximal subgroup of | (C2×#595)⋊Dic3, C4×Dic3×D17, D17×Dic3⋊C4, … |
| maximal normal subgroup of | (C2×#595)⋊Dic3, C4×Dic3×D17, D17×Dic3⋊C4, … |
| maximal quotient of | Dic3×Dic34, #13109019, #13109036, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(816, 135);