Finite Group DatabasebetaFinite Group Databasebeta| order | 7488 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 10616832 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C25×C4 |
| abelian | C22×C42×C9×C13 |
| multiplicative | (ℤ/15105)ˣ, (ℤ/15688)ˣ, (ℤ/16112)ˣ, (ℤ/20140)ˣ, (ℤ/22896)ˣ, (ℤ/23532)ˣ, (ℤ/28620)ˣ, (ℤ/30210)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C22×C3 | C24×C3×C13 |
| socle, prime radical | C24×C3×C13 | C22×C3 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
1494 conjugacy classes of subgroups.
7488 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.