Finite Group DatabasebetaFinite Group Databasebeta| order | 25920 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 2293235712 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C25×C4×C9 |
| abelian | C22×C42×C5×C92 |
| multiplicative | (ℤ/38665)ˣ, (ℤ/51585)ˣ, (ℤ/52725)ˣ, (ℤ/53576)ˣ, (ℤ/54945)ˣ, (ℤ/55024)ˣ, (ℤ/68780)ˣ, (ℤ/70300)ˣ, (ℤ/77330)ˣ, (ℤ/78192)ˣ, (ℤ/80364)ˣ, (ℤ/97740)ˣ, (ℤ/99900)ˣ, (ℤ/103170)ˣ, (ℤ/105450)ˣ, (ℤ/109890)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C22×C32 | C24×C32×C5 |
| socle, prime radical | C24×C32×C5 | C22×C32 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
11454 conjugacy classes of subgroups.
25920 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.