Finite Group DatabasebetaFinite Group Databasebeta| order | 24192 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 82944 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C2×C3 |
| abelian | C2×C3×C7×C9×C64 |
| multiplicative | (ℤ/24511)ˣ, (ℤ/24811)ˣ, (ℤ/28273)ˣ, (ℤ/49022)ˣ, (ℤ/49622)ˣ, (ℤ/56546)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C3×C32 | C22×C32×C7 |
| socle, prime radical | C22×C32×C7 | C3×C32 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
400 conjugacy classes of subgroups.
24192 conjugacy classes. The character table is too large to display.
| automorphism group of | C127×C193, C43×C577 |
| outer automorphism group of | C127×C193, C43×C577 |
Past the SmallGroups library coverage — no SmallGroups id.