Finite Group DatabasebetaFinite Group Databasebeta| order | 24192 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 3567255552 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23×C3×C43 |
| abelian | C2×C3×C43×C7×C9 |
| multiplicative | (ℤ/35815)ˣ, (ℤ/37555)ˣ, (ℤ/41847)ˣ, (ℤ/48285)ˣ, (ℤ/50895)ˣ, (ℤ/55796)ˣ, (ℤ/71630)ˣ, (ℤ/75110)ˣ, (ℤ/83694)ˣ, (ℤ/96570)ˣ, (ℤ/101790)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C23×C3 | C24×C32×C7 |
| socle, prime radical | C24×C32×C7 | C23×C3 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
12720 conjugacy classes of subgroups.
24192 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.