Finite Group DatabasebetaFinite Group Databasebeta| order | 23328 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 62705664 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C26×C3 |
| abelian | C23×C3×C4×C243 |
| multiplicative | (ℤ/50648)ˣ, (ℤ/51135)ˣ, (ℤ/54544)ˣ, (ℤ/68180)ˣ, (ℤ/70128)ˣ, (ℤ/75816)ˣ, (ℤ/75972)ˣ, (ℤ/81648)ˣ, (ℤ/87660)ˣ, (ℤ/102060)ˣ, (ℤ/102270)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C81 | C24×C32 |
| socle, prime radical | C24×C32 | C2×C81 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
2596 conjugacy classes of subgroups.
23328 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.