Finite Group DatabasebetaFinite Group Databasebeta| order | 2256 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) = C23×C4×C23 (order 736) · Inn(G) = C1 · Out(G) = C23×C4×C23 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C1 |
| cyclic | C2256 |
| abelian | C3×C16×C47 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C8 | C2×C3×C47 |
| socle, prime radical | C2×C3×C47 | C8 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
20 conjugacy classes of subgroups.
2256 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C32×C47, C2×C3×C16×C47, C9×C16×C47, … |
| maximal normal subgroup of | C3×C32×C47, C2×C3×C16×C47, C9×C16×C47, … |
| maximal quotient of | C3×C32×C47, C2×C3×C16×C47, C9×C16×C47, … |
Past the SmallGroups library coverage — no SmallGroups id.