Finite Group DatabasebetaFinite Group Databasebeta| order | 11784 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) = C24×C5×C49 (order 3920) · Inn(G) = C1 · Out(G) = C24×C5×C49 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C1 |
| cyclic | C11784 |
| abelian | C3×C8×C491 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C4 | C2×C3×C491 |
| socle, prime radical | C2×C3×C491 | C4 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
16 conjugacy classes of subgroups.
11784 conjugacy classes. The character table is too large to display.
| derived subgroup of | Dic11784, D23568 |
| maximal subgroup of | C3×C16×C491, C2×C3×C8×C491, D11784, … |
| maximal normal subgroup of | C3×C16×C491, C2×C3×C8×C491, D11784, … |
| maximal quotient of | C3×C16×C491, C2×C3×C8×C491 |
Past the SmallGroups library coverage — no SmallGroups id.