Finite Group DatabasebetaFinite Group Databasebeta| order | 24240 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 153600 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23 |
| abelian | C22×C3×C4×C5×C101 |
| multiplicative | (ℤ/33385)ˣ, (ℤ/40029)ˣ, (ℤ/45525)ˣ, (ℤ/53372)ˣ, (ℤ/60700)ˣ, (ℤ/66770)ˣ, (ℤ/80058)ˣ, (ℤ/91050)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2 | C23×C3×C5×C101 |
| socle, prime radical | C23×C3×C5×C101 | C2 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
216 conjugacy classes of subgroups.
24240 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.