Finite Group DatabasebetaFinite Group Databasebeta| order | 23328 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 4514807808 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C26×C33 |
| abelian | C23×C32×C4×C81 |
| multiplicative | (ℤ/44499)ˣ, (ℤ/51345)ˣ, (ℤ/59332)ˣ, (ℤ/76284)ˣ, (ℤ/88452)ˣ, (ℤ/88998)ˣ, (ℤ/102690)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C27 | C24×C33 |
| socle, prime radical | C24×C33 | C2×C27 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
11092 conjugacy classes of subgroups.
23328 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.