Finite Group DatabasebetaFinite Group Databasebeta| order | 17280 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 2967956619264 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C29×C33×C4 |
| abelian | C23×C33×C42×C5 |
| multiplicative | (ℤ/42315)ˣ, (ℤ/44408)ˣ, (ℤ/45045)ˣ, (ℤ/45136)ˣ, (ℤ/56420)ˣ, (ℤ/57096)ˣ, (ℤ/58032)ˣ, (ℤ/61488)ˣ, (ℤ/66612)ˣ, (ℤ/72540)ˣ, (ℤ/76860)ˣ, (ℤ/81900)ˣ, (ℤ/84630)ˣ, (ℤ/90090)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C22 | C25×C33×C5 |
| socle, prime radical | C25×C33×C5 | C22 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
84000 conjugacy classes of subgroups.
17280 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.