Finite Group DatabasebetaFinite Group Databasebeta| order | 23040 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 32469952757760 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C214×C3×C4 |
| abelian | C24×C32×C4×C5×C8 |
| multiplicative | (ℤ/89544)ˣ, (ℤ/96096)ˣ, (ℤ/103320)ˣ, (ℤ/104160)ˣ, (ℤ/110880)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C4 | C26×C32×C5 |
| socle, prime radical | C26×C32×C5 | C2×C4 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
225048 conjugacy classes of subgroups.
23040 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.