Finite Group DatabasebetaFinite Group Databasebeta| order | 816 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | #67×D17 |
| Fitting | C22×C3×C17 ⋊ C22 |
| Hall | C3×C17 ⋊ C2×D4 |
| Sylow | C17 ⋊ C2×#67 |
| Sylow | C3 ⋊ D4×D17 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×D3×D17 |
| commutator, socle, cosocle | C2×C3×C17 | C23 |
| Fitting | C22×C3×C17 | C22 |
| hypercenter | C22 | D3×D17 |
| hypocenter | C3×C17 | C2×D4 |
| LCS | G ▷ C2×C3×C17 ▷ C3×C17 | |
| UCS | C1 ◁ C2 ◁ C22 | |
108 conjugacy classes of subgroups.
| transitive degree | μt(G) = 204 |
90 conjugacy classes — view the full character table.
| maximal subgroup of | #67×#595, #67⋊#595, D17×#235, … |
| maximal normal subgroup of | #67×#595, #67⋊#595, D17×#235, … |
| maximal quotient of | D17×Dic3⋊C4, #13109123, #13109124, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(816, 145);