Finite Group DatabasebetaFinite Group Databasebeta| order | 6174 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) = C22×C32×C49 (order 1764) · Inn(G) = C1 · Out(G) = C22×C32×C49 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C1 |
| cyclic | C6174 |
| abelian | C2×C9×C343 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C3×C49 | C2×C3×C7 |
| socle, prime radical | C2×C3×C7 | C3×C49 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
24 conjugacy classes of subgroups.
6174 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×C9×C343, C22×C9×C343, C2×C27×C343, … |
| maximal normal subgroup of | C4×C9×C343, C22×C9×C343, C2×C27×C343, … |
| maximal quotient of | C4×C9×C343, C22×C9×C343, C2×C27×C343, … |
Past the SmallGroups library coverage — no SmallGroups id.