Finite Group DatabasebetaFinite Group Databasebeta| order | 816 |
| isoclinism | isoclinic class of D3×#595 |
| 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 ⋊ #63242 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D3×#595 |
| commutator, hypocenter | C3×C17 | C2×C8 |
| Fitting, socle | C2×C3×C17 | C2×C4 |
| prime radical | C2×D51 | C4 |
| cosocle | C3×Dic17 | C22 |
| LCS | G ▷ C3×C17 | |
| UCS | C1 ◁ C2 | |
44 conjugacy classes of subgroups.
| transitive degree | μt(G) = 408 |
Polycyclic presentation:
2^4,3,17|a^2=c,b^2=d,c^2=d,f^a=f^13,e^b=e^2,f^c=f^1648 conjugacy classes — view the full character table.
| maximal subgroup of | #13109610, #13109612, D3×#63242, … |
| maximal normal subgroup of | #13109610, #13109612, D3×#63242, … |
| maximal quotient of | #13108901, #13108903, Dic3×#3624, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(816, 95);