Finite Group DatabasebetaFinite Group Databasebeta| order | 23040 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 3145728 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C22×C3×C4 |
| abelian | C2×C32×C4×C5×C64 |
| multiplicative | (ℤ/27599)ˣ, (ℤ/29915)ˣ, (ℤ/33775)ˣ, (ℤ/35319)ˣ, (ℤ/43425)ˣ, (ℤ/47092)ˣ, (ℤ/55198)ˣ, (ℤ/59830)ˣ, (ℤ/67550)ˣ, (ℤ/70638)ˣ, (ℤ/86850)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C32 | C23×C32×C5 |
| socle, prime radical | C23×C32×C5 | C2×C32 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
1944 conjugacy classes of subgroups.
23040 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.