Finite Group DatabasebetaFinite Group Databasebeta| order | 3456 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 21233664 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C25×C3×C4 |
| abelian | C22×C3×C4×C8×C9 |
| multiplicative | (ℤ/7592)ˣ, (ℤ/7665)ˣ, (ℤ/7904)ˣ, (ℤ/8176)ˣ, (ℤ/8288)ˣ, (ℤ/10220)ˣ, (ℤ/10512)ˣ, (ℤ/10656)ˣ, (ℤ/11232)ˣ, (ℤ/11388)ˣ, (ℤ/13140)ˣ, (ℤ/15330)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C3×C4 | C24×C32 |
| socle, prime radical | C24×C32 | C2×C3×C4 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
3800 conjugacy classes of subgroups.
3456 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.