Finite Group DatabasebetaFinite Group Databasebeta| order | 28800 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 491520 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C22×C4 |
| abelian | C2×C4×C9×C16×C25 |
| multiplicative | (ℤ/32623)ˣ, (ℤ/38095)ˣ, (ℤ/40375)ˣ, (ℤ/44511)ˣ, (ℤ/46359)ˣ, (ℤ/54135)ˣ, (ℤ/57375)ˣ, (ℤ/59348)ˣ, (ℤ/65246)ˣ, (ℤ/76190)ˣ, (ℤ/80750)ˣ, (ℤ/89022)ˣ, (ℤ/92718)ˣ, (ℤ/108270)ˣ, (ℤ/114750)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C3×C5×C8 | C23×C3×C5 |
| socle, prime radical | C23×C3×C5 | C2×C3×C5×C8 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
972 conjugacy classes of subgroups.
28800 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.