Finite Group DatabasebetaFinite Group Databasebeta| order | 28320 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 9977856 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C26 |
| abelian | C23×C3×C4×C5×C59 |
| multiplicative | (ℤ/62392)ˣ, (ℤ/66136)ˣ, (ℤ/84984)ˣ, (ℤ/85032)ˣ, (ℤ/93588)ˣ, (ℤ/99204)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2 | C24×C3×C5×C59 |
| socle, prime radical | C24×C3×C5×C59 | C2 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
944 conjugacy classes of subgroups.
28320 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.