Finite Group DatabasebetaFinite Group Databasebeta| order | 6240 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 12288 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C4 |
| abelian | C3×C4×C5×C8×C13 |
| multiplicative | (ℤ/6437)ˣ, (ℤ/6773)ˣ, (ℤ/6929)ˣ, (ℤ/7825)ˣ, (ℤ/12874)ˣ, (ℤ/13546)ˣ, (ℤ/13858)ˣ, (ℤ/15650)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C4 | C22×C3×C5×C13 |
| socle, prime radical | C22×C3×C5×C13 | C2×C4 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
176 conjugacy classes of subgroups.
6240 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.