Finite Group DatabasebetaFinite Group Databasebeta| order | 23040 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 49152 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C4 |
| abelian | C4×C5×C9×C128 |
| multiplicative | (ℤ/23717)ˣ, (ℤ/28825)ˣ, (ℤ/47434)ˣ, (ℤ/57650)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C3×C64 | C22×C3×C5 |
| socle, prime radical | C22×C3×C5 | C2×C3×C64 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
300 conjugacy classes of subgroups.
23040 conjugacy classes. The character table is too large to display.
| automorphism group of | C37×C641 |
| outer automorphism group of | C37×C641 |
Past the SmallGroups library coverage — no SmallGroups id.