Finite Group DatabasebetaFinite Group Databasebeta| order | 28800 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 3932160 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C22×C3×C4 |
| abelian | C2×C32×C4×C16×C25 |
| multiplicative | (ℤ/33371)ˣ, (ℤ/36491)ˣ, (ℤ/42035)ˣ, (ℤ/46839)ˣ, (ℤ/46917)ˣ, (ℤ/54045)ˣ, (ℤ/62452)ˣ, (ℤ/66742)ˣ, (ℤ/72982)ˣ, (ℤ/84070)ˣ, (ℤ/93678)ˣ, (ℤ/93834)ˣ, (ℤ/108090)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C5×C8 | C23×C32×C5 |
| socle, prime radical | C23×C32×C5 | C2×C5×C8 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
1944 conjugacy classes of subgroups.
28800 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.