Finite Group DatabasebetaFinite Group Databasebeta| order | 24480 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 12288 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C2 |
| abelian | C2×C5×C9×C16×C17 |
| multiplicative | (ℤ/25859)ˣ, (ℤ/26027)ˣ, (ℤ/36723)ˣ, (ℤ/36747)ˣ, (ℤ/48964)ˣ, (ℤ/51718)ˣ, (ℤ/52054)ˣ, (ℤ/73446)ˣ, (ℤ/73494)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C3×C8 | C22×C3×C5×C17 |
| socle, prime radical | C22×C3×C5×C17 | C3×C8 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
168 conjugacy classes of subgroups.
24480 conjugacy classes. The character table is too large to display.
| automorphism group of | C19×C1361, C17×C1531 |
| outer automorphism group of | C19×C1361, C17×C1531 |
Past the SmallGroups library coverage — no SmallGroups id.