Finite Group DatabasebetaFinite Group Databasebeta| order | 28416 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 28311552 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C25×C4 |
| abelian | C22×C3×C4×C16×C37 |
| multiplicative | (ℤ/53193)ˣ, (ℤ/56865)ˣ, (ℤ/60656)ˣ, (ℤ/61672)ˣ, (ℤ/62265)ˣ, (ℤ/66416)ˣ, (ℤ/66752)ˣ, (ℤ/70924)ˣ, (ℤ/71080)ˣ, (ℤ/71360)ˣ, (ℤ/75820)ˣ, (ℤ/83020)ˣ, (ℤ/85296)ˣ, (ℤ/85392)ˣ, (ℤ/85824)ˣ, (ℤ/91188)ˣ, (ℤ/92508)ˣ, (ℤ/106386)ˣ, (ℤ/106620)ˣ, (ℤ/106740)ˣ, (ℤ/113730)ˣ, (ℤ/124530)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C8 | C24×C3×C37 |
| socle, prime radical | C24×C3×C37 | C2×C8 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
2044 conjugacy classes of subgroups.
28416 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.