Finite Group DatabasebetaFinite Group Databasebeta| order | 18576 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 870912 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23×C3 |
| abelian | C22×C3×C4×C9×C43 |
| multiplicative | (ℤ/23009)ˣ, (ℤ/29583)ˣ, (ℤ/32529)ˣ, (ℤ/32697)ˣ, (ℤ/43372)ˣ, (ℤ/46018)ˣ, (ℤ/55764)ˣ, (ℤ/59166)ˣ, (ℤ/65058)ˣ, (ℤ/65394)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C3 | C23×C32×C43 |
| socle, prime radical | C23×C32×C43 | C2×C3 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
540 conjugacy classes of subgroups.
18576 conjugacy classes. The character table is too large to display.
| automorphism group of | C7×C27×C173 |
| outer automorphism group of | C7×C27×C173 |
Past the SmallGroups library coverage — no SmallGroups id.