Finite Group DatabasebetaFinite Group Databasebeta| order | 816 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Hall | C3×C17 ⋊ Q16 |
| Sylow | C17 ⋊ Dic12 |
| Sylow | C3 ⋊ #63231 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | #87975 |
| commutator, Fitting, cosocle | C3×C4×C17 | C22 |
| Frattini, hypercenter | C4 | D3×D17 |
| socle, prime radical | C2×C3×C17 | D4 |
| hypocenter | C3×C17 | Q16 |
| LCS | G ▷ C3×C4×C17 ▷ C2×C3×C17 ▷ C3×C17 | |
| UCS | C1 ◁ C2 ◁ C4 | |
36 conjugacy classes of subgroups.
| minimal degree | μ(G) = 36 |
| transitive degree | μt(G) = 816 |
Polycyclic presentation:
2^4,3,17|a^2=c,b^2=d,c^2=d,b^a=bc,f^a=f^16,c^b=cd,e^b=e^287 conjugacy classes — view the full character table.
| maximal subgroup of | D17×Dic12, #13108997, #13108998, … |
| maximal normal subgroup of | D17×Dic12, #13108997, #13108998, … |
| maximal quotient of | #13108714, #13108716, #13108729, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(816, 24);