Finite Group DatabasebetaFinite Group Databasebeta| order | 7776 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 20901888 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C26×C3 |
| abelian | C23×C3×C4×C81 |
| multiplicative | (ℤ/16952)ˣ, (ℤ/17115)ˣ, (ℤ/18256)ˣ, (ℤ/22820)ˣ, (ℤ/23472)ˣ, (ℤ/25272)ˣ, (ℤ/25428)ˣ, (ℤ/27216)ˣ, (ℤ/29340)ˣ, (ℤ/34020)ˣ, (ℤ/34230)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C27 | C24×C32 |
| socle, prime radical | C24×C32 | C2×C27 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
2124 conjugacy classes of subgroups.
7776 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.