Finite Group DatabasebetaFinite Group Databasebeta| order | 6912 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 7077888 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C25×C4 |
| abelian | C22×C4×C16×C27 |
| multiplicative | (ℤ/14824)ˣ, (ℤ/17320)ˣ, (ℤ/20784)ˣ, (ℤ/20928)ˣ, (ℤ/22032)ˣ, (ℤ/22236)ˣ, (ℤ/25920)ˣ, (ℤ/25980)ˣ, (ℤ/27540)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C8×C9 | C24×C3 |
| socle, prime radical | C24×C3 | C2×C8×C9 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
2044 conjugacy classes of subgroups.
6912 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.