Finite Group DatabasebetaFinite Group Databasebeta| order | 816 |
| isoclinism | isoclinic class of D3×D17 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| derived, Hall | C3×C17 ⋊ C2×C8 |
| Sylow | C17 ⋊ D3×C8 |
| Sylow | C3 ⋊ C8×D17 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C4 | D3×D17 |
| commutator, hypocenter | C3×C17 | C2×C8 |
| Fitting, cosocle | C3×C4×C17 | C22 |
| socle | C2×C3×C17 | C2×C4 |
| prime radical | C2×D51 | C4 |
| LCS | G ▷ C3×C17 | |
| UCS | C1 ◁ C4 | |
44 conjugacy classes of subgroups.
| transitive degree | μt(G) = 408 |
Polycyclic presentation:
2^4,3,17|a^2=c,b^2=c,c^2=d,f^a=f^16,e^b=e^2120 conjugacy classes — view the full character table.
| maximal subgroup of | #13108901, #13108903, D3×C8×D17, … |
| maximal normal subgroup of | #13108901, #13108903, D3×C8×D17, … |
| maximal quotient of | #13108674, #13108677, #13108692, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(816, 9);