Finite Group DatabasebetaFinite Group Databasebeta| order | 28800 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 94371840 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C22×C3×C4×C5 |
| abelian | C2×C32×C4×C52×C16 |
| multiplicative | (ℤ/32147)ˣ, (ℤ/34463)ˣ, (ℤ/37355)ˣ, (ℤ/42175)ˣ, (ℤ/44103)ˣ, (ℤ/54225)ˣ, (ℤ/58804)ˣ, (ℤ/64294)ˣ, (ℤ/68926)ˣ, (ℤ/74710)ˣ, (ℤ/84350)ˣ, (ℤ/88206)ˣ, (ℤ/108450)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C8 | C23×C32×C52 |
| socle, prime radical | C23×C32×C52 | C2×C8 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
5184 conjugacy classes of subgroups.
28800 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.