Finite Group DatabasebetaFinite Group Databasebeta| order | 29376 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 1854972887040 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C210×C33 |
| abelian | C24×C33×C4×C17 |
| multiplicative | (ℤ/74984)ˣ, (ℤ/96408)ˣ, (ℤ/103824)ˣ, (ℤ/112476)ˣ, (ℤ/129780)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2 | C25×C33×C17 |
| socle, prime radical | C25×C33×C17 | C2 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
38136 conjugacy classes of subgroups.
29376 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.