Finite Group DatabasebetaFinite Group Databasebeta| order | 7040 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 7864320 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C25×C4 |
| abelian | C22×C4×C5×C8×C11 |
| multiplicative | (ℤ/14145)ˣ, (ℤ/14685)ˣ, (ℤ/15088)ˣ, (ℤ/15664)ˣ, (ℤ/17800)ˣ, (ℤ/18400)ˣ, (ℤ/18860)ˣ, (ℤ/19360)ˣ, (ℤ/19580)ˣ, (ℤ/26700)ˣ, (ℤ/28290)ˣ, (ℤ/29370)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C4 | C24×C5×C11 |
| socle, prime radical | C24×C5×C11 | C2×C4 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
1520 conjugacy classes of subgroups.
7040 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.