Finite Group DatabasebetaFinite Group Databasebeta| order | 7680 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 1409286144 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C29×C4 |
| abelian | C23×C3×C4×C5×C16 |
| multiplicative | (ℤ/19448)ˣ, (ℤ/19635)ˣ, (ℤ/20944)ˣ, (ℤ/21080)ˣ, (ℤ/23800)ˣ, (ℤ/24640)ˣ, (ℤ/24888)ˣ, (ℤ/25296)ˣ, (ℤ/26180)ˣ, (ℤ/26928)ˣ, (ℤ/27456)ˣ, (ℤ/28920)ˣ, (ℤ/29172)ˣ, (ℤ/29760)ˣ, (ℤ/30600)ˣ, (ℤ/31620)ˣ, (ℤ/31680)ˣ, (ℤ/33600)ˣ, (ℤ/33660)ˣ, (ℤ/35700)ˣ, (ℤ/39270)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C8 | C25×C3×C5 |
| socle, prime radical | C25×C3×C5 | C2×C8 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
12552 conjugacy classes of subgroups.
7680 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.