Finite Group DatabasebetaFinite Group Databasebeta| order | 816 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | (C2×D3)⋊#595 |
| unambiguous semidirect product | (C2×#595)⋊D3 |
| Hall | C3×C17 ⋊ C22⋊C4 |
| Sylow | C17 ⋊ (C2×D3)⋊C4 |
| Sylow | C3 ⋊ C22⋊#595 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D3×#595 |
| commutator, Fitting, socle | C2×C3×C17 | C2×C4 |
| prime radical | C2×D3×D17 | C2 |
| cosocle | C2×C3×D17 | C22 |
| hypocenter | C3×C17 | C22⋊C4 |
| LCS | G ▷ C2×C3×C17 ▷ C3×C17 | |
| UCS | C1 ◁ C2 | |
68 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 204 |
Polycyclic presentation:
2^4,3,17|a^2=c,b^a=bd,f^a=f^13,e^b=e^2,f^c=f^1642 conjugacy classes — view the full character table.
| maximal subgroup of | #13109649, #13109651, D12×#595, … |
| maximal normal subgroup of | #13109649, #13109651, D12×#595, … |
| maximal quotient of | #13108888, #13108889, #13108890, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(816, 92);