Finite Group DatabasebetaFinite Group Databasebeta| order | 24576 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 824633720832 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C27×C42×C16 |
| abelian | C22×C3×C4×C16×C32 |
| multiplicative | (ℤ/65960)ˣ, (ℤ/76160)ˣ, (ℤ/79152)ˣ, (ℤ/84864)ˣ, (ℤ/93120)ˣ, (ℤ/97920)ˣ, (ℤ/98940)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C8×C16 | C25×C3 |
| socle, prime radical | C25×C3 | C2×C8×C16 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
88860 conjugacy classes of subgroups.
24576 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.