Finite Group DatabasebetaFinite Group Databasebeta| order | 24720 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 156672 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23 |
| abelian | C22×C3×C4×C5×C103 |
| multiplicative | (ℤ/34045)ˣ, (ℤ/36085)ˣ, (ℤ/40209)ˣ, (ℤ/40821)ˣ, (ℤ/46395)ˣ, (ℤ/46425)ˣ, (ℤ/53612)ˣ, (ℤ/54428)ˣ, (ℤ/61900)ˣ, (ℤ/68090)ˣ, (ℤ/72170)ˣ, (ℤ/80418)ˣ, (ℤ/81642)ˣ, (ℤ/92790)ˣ, (ℤ/92850)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2 | C23×C3×C5×C103 |
| socle, prime radical | C23×C3×C5×C103 | C2 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
216 conjugacy classes of subgroups.
24720 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.