Finite Group DatabasebetaFinite Group Databasebeta| order | 23280 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 147456 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23 |
| abelian | C22×C3×C4×C5×C97 |
| multiplicative | (ℤ/29953)ˣ, (ℤ/33985)ˣ, (ℤ/36177)ˣ, (ℤ/37869)ˣ, (ℤ/38511)ˣ, (ℤ/43695)ˣ, (ℤ/46568)ˣ, (ℤ/48236)ˣ, (ℤ/50492)ˣ, (ℤ/59906)ˣ, (ℤ/67970)ˣ, (ℤ/69852)ˣ, (ℤ/72354)ˣ, (ℤ/75738)ˣ, (ℤ/77022)ˣ, (ℤ/87390)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2 | C23×C3×C5×C97 |
| socle, prime radical | C23×C3×C5×C97 | C2 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
216 conjugacy classes of subgroups.
23280 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.