Finite Group DatabasebetaFinite Group Databasebeta| order | 12000 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) = C22×C4×C8×C25 (order 3200) · Inn(G) = C1 · Out(G) = C22×C4×C8×C25 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C1 |
| cyclic | C12000 |
| abelian | C3×C32×C125 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C16×C25 | C2×C3×C5 |
| socle, prime radical | C2×C3×C5 | C16×C25 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
48 conjugacy classes of subgroups.
12000 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.