Finite Group DatabasebetaFinite Group Databasebeta| order | 7168 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 28991029248 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C27×C43 |
| abelian | C22×C42×C7×C16 |
| multiplicative | (ℤ/19720)ˣ, (ℤ/23664)ˣ, (ℤ/27120)ˣ, (ℤ/27840)ˣ, (ℤ/29580)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C22×C8 | C25×C7 |
| socle, prime radical | C25×C7 | C22×C8 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
18282 conjugacy classes of subgroups.
7168 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.