Finite Group DatabasebetaFinite Group Databasebeta| order | 816 |
| isoclinism | isoclinic class of #226 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C17 · Schur multiplier (H2) = C1 |
| direct product | C17×#226 |
| subgroup | G/H | |
|---|---|---|
| center, socle, hypercenter | C2×C17 | S4 |
| commutator, cosocle, hypocenter | SL(2,𝔽3) | C2×C17 |
| Frattini | C2 | C17×S4 |
| Fitting | Q8×C17 | D3 |
| prime radical | C17×SL(2,𝔽3) | C2 |
| LCS | G ▷ SL(2,𝔽3) | |
| UCS | C1 ◁ C2×C17 | |
26 conjugacy classes of subgroups.
| transitive degree | μt(G) = 272 |
136 conjugacy classes — view the full character table.
| maximal subgroup of | #13109619, #13109621, D17×#226, … |
| maximal normal subgroup of | #13109619, #13109621, D17×#226, … |
| maximal quotient of | C17×#859, C2×C17×#226 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(816, 98);