Finite Group DatabasebetaFinite Group Databasebeta| order | 2304 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 2359296 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C25×C4 |
| abelian | C22×C4×C9×C16 |
| multiplicative | (ℤ/4845)ˣ, (ℤ/5032)ˣ, (ℤ/5168)ˣ, (ℤ/6080)ˣ, (ℤ/6460)ˣ, (ℤ/7104)ˣ, (ℤ/7344)ˣ, (ℤ/7548)ˣ, (ℤ/8640)ˣ, (ℤ/9180)ˣ, (ℤ/9690)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C3×C8 | C24×C3 |
| socle, prime radical | C24×C3 | C2×C3×C8 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
1533 conjugacy classes of subgroups.
2304 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.