Finite Group DatabasebetaFinite Group Databasebeta| order | 23328 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 2176782336 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C22×C32×C4×C9 |
| abelian | C2×C3×C42×C9×C27 |
| multiplicative | (ℤ/26923)ˣ, (ℤ/28231)ˣ, (ℤ/36297)ˣ, (ℤ/38259)ˣ, (ℤ/38961)ˣ, (ℤ/53846)ˣ, (ℤ/56462)ˣ, (ℤ/72594)ˣ, (ℤ/76518)ˣ, (ℤ/77922)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C22×C3×C9 | C23×C33 |
| socle, prime radical | C23×C33 | C22×C3×C9 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
10908 conjugacy classes of subgroups.
23328 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.