Finite Group DatabasebetaFinite Group Databasebeta| order | 13824 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 5750784 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C2×C33 |
| abelian | C2×C33×C256 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C128 | C22×C33 |
| socle, prime radical | C22×C33 | C128 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
728 conjugacy classes of subgroups.
13824 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C33×C512, C33×C4×C256, C22×C33×C256 |
| maximal normal subgroup of | C2×C33×C512, C33×C4×C256, C22×C33×C256 |
| maximal quotient of | C2×C33×C512, C33×C4×C256, C22×C33×C256 |
Past the SmallGroups library coverage — no SmallGroups id.