Finite Group DatabasebetaFinite Group Databasebeta| order | 24000 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 8192000 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C22×C4×C5 |
| abelian | C2×C3×C4×C5×C8×C25 |
| multiplicative | (ℤ/28987)ˣ, (ℤ/30955)ˣ, (ℤ/33055)ˣ, (ℤ/35875)ˣ, (ℤ/37269)ˣ, (ℤ/45075)ˣ, (ℤ/46125)ˣ, (ℤ/57974)ˣ, (ℤ/60100)ˣ, (ℤ/61910)ˣ, (ℤ/66110)ˣ, (ℤ/71750)ˣ, (ℤ/74538)ˣ, (ℤ/90150)ˣ, (ℤ/92250)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C4×C5 | C23×C3×C52 |
| socle, prime radical | C23×C3×C52 | C2×C4×C5 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
2268 conjugacy classes of subgroups.
24000 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.