Finite Group DatabasebetaFinite Group Databasebeta| order | 816 |
| isoclinism | isoclinic class of #595 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C8 · Schur multiplier (H2) = C2 |
| direct product | C2×C3×#3624 |
| derived, Sylow | C17 ⋊ C2×C3×C8 |
| Hall | C3×C17 ⋊ C2×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C3 | #595 |
| commutator, hypocenter | C17 | C2×C3×C8 |
| Frattini | C2 | C2×C3×#595 |
| Fitting, socle, prime radical | C22×C3×C17 | C4 |
| cosocle | Dic17 | C22×C3 |
| LCS | G ▷ C17 | |
| UCS | C1 ◁ C22×C3 | |
44 conjugacy classes of subgroups.
| transitive degree | μt(G) = 816 |
96 conjugacy classes — view the full character table.
| maximal subgroup of | Dic3×#3624, #13108906, (C2×D3)⋊#3624, … |
| maximal normal subgroup of | Dic3×#3624, #13108906, (C2×D3)⋊#3624, … |
| maximal quotient of | C2×C3×#63216, C3×#10587538, C3×C4×#3624, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(816, 111);