Finite Group DatabasebetaFinite Group Databasebeta| order | 816 |
| isoclinism | isoclinic class of Dic34 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | C2×C3×C22⋊D17 |
| Fitting | C23×C3×C17 ⋊ C2 |
| Hall | C3×C17 ⋊ C2×D4 |
| Sylow | C17 ⋊ C2×C3×D4 |
108 conjugacy classes of subgroups.
| transitive degree | μt(G) = 408 |
222 conjugacy classes — view the full character table.
| maximal subgroup of | #13108736, C3×#10587477, C3×#10587551, … |
| maximal normal subgroup of | #13108736, C3×#10587477, C3×#10587551, … |
| maximal quotient of | C2×C3×#63225, C3×#10587610, C2×C3×#63227, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(816, 160);