Finite Group DatabasebetaFinite Group Databasebeta| order | 24192 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 127401984 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C25×C3×C4 |
| abelian | C22×C3×C4×C7×C8×C9 |
| multiplicative | (ℤ/44457)ˣ, (ℤ/47085)ˣ, (ℤ/50224)ˣ, (ℤ/50912)ˣ, (ℤ/52832)ˣ, (ℤ/53655)ˣ, (ℤ/57232)ˣ, (ℤ/58016)ˣ, (ℤ/59276)ˣ, (ℤ/62780)ˣ, (ℤ/71540)ˣ, (ℤ/76212)ˣ, (ℤ/88914)ˣ, (ℤ/94170)ˣ, (ℤ/107310)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C3×C4 | C24×C32×C7 |
| socle, prime radical | C24×C32×C7 | C2×C3×C4 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
7600 conjugacy classes of subgroups.
24192 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.