Finite Group DatabasebetaFinite Group Databasebeta| order | 7200 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 1474560 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C22×C3×C4 |
| abelian | C2×C32×C42×C25 |
| multiplicative | (ℤ/9191)ˣ, (ℤ/9815)ˣ, (ℤ/11375)ˣ, (ℤ/11817)ˣ, (ℤ/14625)ˣ, (ℤ/18382)ˣ, (ℤ/19630)ˣ, (ℤ/22750)ˣ, (ℤ/23634)ˣ, (ℤ/29250)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C22×C5 | C23×C32×C5 |
| socle, prime radical | C23×C32×C5 | C22×C5 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
972 conjugacy classes of subgroups.
7200 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.