Finite Group DatabasebetaFinite Group Databasebeta| order | 29376 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 17836277760 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C210×C3 |
| abelian | C24×C3×C4×C9×C17 |
| multiplicative | (ℤ/78280)ˣ, (ℤ/85960)ˣ, (ℤ/91464)ˣ, (ℤ/93936)ˣ, (ℤ/95784)ˣ, (ℤ/102984)ˣ, (ℤ/103152)ˣ, (ℤ/110520)ˣ, (ℤ/111240)ˣ, (ℤ/117420)ˣ, (ℤ/128940)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C3 | C25×C32×C17 |
| socle, prime radical | C25×C32×C17 | C2×C3 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
13620 conjugacy classes of subgroups.
29376 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.