Finite Group DatabasebetaFinite Group Databasebeta| order | 24336 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 241532928 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23×C3×C13 |
| abelian | C22×C32×C4×C132 |
| multiplicative | (ℤ/29309)ˣ, (ℤ/37209)ˣ, (ℤ/37683)ˣ, (ℤ/40053)ˣ, (ℤ/49612)ˣ, (ℤ/53404)ˣ, (ℤ/58618)ˣ, (ℤ/74418)ˣ, (ℤ/75366)ˣ, (ℤ/80106)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2 | C23×C32×C132 |
| socle, prime radical | C23×C32×C132 | C2 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
2592 conjugacy classes of subgroups.
24336 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.