Finite Group DatabasebetaFinite Group Databasebeta| order | 30912 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 38928384 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C25×C4 |
| abelian | C22×C3×C42×C7×C23 |
| multiplicative | (ℤ/47705)ˣ, (ℤ/53157)ˣ, (ℤ/60465)ˣ, (ℤ/61335)ˣ, (ℤ/64264)ˣ, (ℤ/64496)ˣ, (ℤ/70876)ˣ, (ℤ/77320)ˣ, (ℤ/77360)ˣ, (ℤ/80620)ˣ, (ℤ/92784)ˣ, (ℤ/95410)ˣ, (ℤ/96396)ˣ, (ℤ/106314)ˣ, (ℤ/115980)ˣ, (ℤ/120930)ˣ, (ℤ/122670)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C22 | C24×C3×C7×C23 |
| socle, prime radical | C24×C3×C7×C23 | C22 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
1992 conjugacy classes of subgroups.
30912 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.