Finite Group DatabasebetaFinite Group Databasebeta| order | 10560 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 825753600 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C210 |
| abelian | C24×C3×C4×C5×C11 |
| multiplicative | (ℤ/26312)ˣ, (ℤ/26565)ˣ, (ℤ/28336)ˣ, (ℤ/28520)ˣ, (ℤ/29480)ˣ, (ℤ/32200)ˣ, (ℤ/33672)ˣ, (ℤ/33880)ˣ, (ℤ/34224)ˣ, (ℤ/35376)ˣ, (ℤ/35420)ˣ, (ℤ/36432)ˣ, (ℤ/37752)ˣ, (ℤ/39468)ˣ, (ℤ/39720)ˣ, (ℤ/40200)ˣ, (ℤ/40656)ˣ, (ℤ/41400)ˣ, (ℤ/42780)ˣ, (ℤ/43560)ˣ, (ℤ/44220)ˣ, (ℤ/45540)ˣ, (ℤ/48300)ˣ, (ℤ/50820)ˣ, (ℤ/53130)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2 | C25×C3×C5×C11 |
| socle, prime radical | C25×C3×C5×C11 | C2 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
5448 conjugacy classes of subgroups.
10560 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.