Finite Group DatabasebetaFinite Group Databasebeta| order | 11664 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) = C22×C4×C243 (order 3888) · Inn(G) = C1 · Out(G) = C22×C4×C243 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C1 |
| cyclic | C11664 |
| abelian | C16×C729 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C8×C243 | C2×C3 |
| socle, prime radical | C2×C3 | C8×C243 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
35 conjugacy classes of subgroups.
11664 conjugacy classes. The character table is too large to display.
| derived subgroup of | Dic11664, D23328 |
| maximal subgroup of | C32×C729, C2×C16×C729, D11664, … |
| maximal normal subgroup of | C32×C729, C2×C16×C729, D11664, … |
| maximal quotient of | C32×C729, C2×C16×C729 |
Past the SmallGroups library coverage — no SmallGroups id.