Finite Group DatabasebetaFinite Group Databasebeta| order | 24576 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 8388608 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C22×C16 |
| abelian | C2×C3×C16×C256 |
| multiplicative | (ℤ/30583)ˣ, (ℤ/39219)ˣ, (ℤ/39321)ˣ, (ℤ/49216)ˣ, (ℤ/52292)ˣ, (ℤ/61166)ˣ, (ℤ/78438)ˣ, (ℤ/78642)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C8×C128 | C23×C3 |
| socle, prime radical | C23×C3 | C8×C128 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
1628 conjugacy classes of subgroups.
24576 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.