Finite Group DatabasebetaFinite Group Databasebeta| order | 816 |
| isoclinism | isoclinic class of D17 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23 |
| direct product | C22×C3×Dic17 |
| derived, Sylow | C17 ⋊ C22×C3×C4 |
| Hall | C3×C17 ⋊ C22×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23×C3 | D17 |
| commutator, hypocenter | C17 | C22×C3×C4 |
| Frattini | C2 | C22×C3×D17 |
| Fitting, socle, prime radical | C23×C3×C17 | C2 |
| cosocle | C2×C17 | C23×C3 |
| LCS | G ▷ C17 | |
| UCS | C1 ◁ C23×C3 | |
108 conjugacy classes of subgroups.
| transitive degree | μt(G) = 816 |
240 conjugacy classes — view the full character table.
| maximal subgroup of | #13108735, C3×#10587502, C3×C22⋊#3624, … |
| maximal normal subgroup of | #13108735, C3×#10587502, C3×C22⋊#3624, … |
| maximal quotient of | C22×C3×#3622, C2×C3×#63223, C2×C3×C4×Dic17, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(816, 159);