Finite Group DatabasebetaFinite Group Databasebeta| order | 11664 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 46656 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C4 |
| abelian | C42×C729 |
| multiplicative | (ℤ/14585)ˣ, (ℤ/29170)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C22×C243 | C22×C3 |
| socle, prime radical | C22×C3 | C22×C243 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
105 conjugacy classes of subgroups.
11664 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×C8×C729, C2×C42×C729 |
| maximal normal subgroup of | C4×C8×C729, C2×C42×C729 |
| maximal quotient of | C4×C8×C729, C2×C42×C729 |
| automorphism group of | C5×C2917 |
| outer automorphism group of | C5×C2917 |
Past the SmallGroups library coverage — no SmallGroups id.