Finite Group DatabasebetaFinite Group Databasebeta| order | 816 |
| isoclinism | isoclinic class of D17 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C42 · Schur multiplier (H2) = C4 |
| direct product | C3×C4×Dic17 |
| derived, Sylow | C17 ⋊ C3×C42 |
| Hall | C3×C17 ⋊ C42 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3×C4 | D17 |
| commutator, hypocenter | C17 | C3×C42 |
| Frattini | C22 | C2×C3×D17 |
| Fitting | C2×C3×C4×C17 | C2 |
| socle, prime radical | C22×C3×C17 | C22 |
| cosocle | C22×C17 | C22×C3 |
| LCS | G ▷ C17 | |
| UCS | C1 ◁ C2×C3×C4 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 816 |
240 conjugacy classes — view the full character table.
| maximal subgroup of | C3⋊C8×Dic17, #13108693, #13108719, … |
| maximal normal subgroup of | C3⋊C8×Dic17, #13108693, #13108719, … |
| maximal quotient of | C3×C4×#3622, C3×#10587474, C3×C8×Dic17, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(816, 40);