Finite Group DatabasebetaFinite Group Databasebeta| order | 816 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | SL(2,𝔽3)×D17 |
| unambiguous semidirect product | C17⋊(C2×SL(2,𝔽3)) |
| unambiguous semidirect product | (Q8×D17)⋊C3 |
| Fitting, derived | Q8×C17 ⋊ C2×C3 |
| Hall | Q8×D17 ⋊ C3 |
| Sylow | C17 ⋊ C2×SL(2,𝔽3) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | A4×D17 |
| commutator, Fitting, cosocle, hypocenter | Q8×C17 | C2×C3 |
| socle | C2×C17 | C2×A4 |
| LCS | G ▷ Q8×C17 | |
| UCS | C1 ◁ C2 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 136 |
70 conjugacy classes — view the full character table.
| maximal subgroup of | #13109614, SL(2,𝔽3)×#595, D17×#226, … |
| maximal normal subgroup of | #13109614, SL(2,𝔽3)×#595, D17×#226, … |
| maximal quotient of | SL(2,𝔽3)×Dic17, C2×SL(2,𝔽3)×D17 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(816, 105);