Finite Group DatabasebetaFinite Group Databasebeta| order | 28512 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 59719680 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C22×C4×C9 |
| abelian | C2×C42×C92×C11 |
| multiplicative | (ℤ/36815)ˣ, (ℤ/37715)ˣ, (ℤ/44067)ˣ, (ℤ/53595)ˣ, (ℤ/58756)ˣ, (ℤ/73630)ˣ, (ℤ/75430)ˣ, (ℤ/88134)ˣ, (ℤ/107190)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C22×C32 | C23×C32×C11 |
| socle, prime radical | C23×C32×C11 | C22×C32 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
2484 conjugacy classes of subgroups.
28512 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.