Finite Group DatabasebetaFinite Group Databasebeta| order | 21504 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 18874368 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C25×C4 |
| abelian | C22×C3×C4×C7×C64 |
| multiplicative | (ℤ/44776)ˣ, (ℤ/46696)ˣ, (ℤ/47145)ˣ, (ℤ/50288)ˣ, (ℤ/51968)ˣ, (ℤ/55040)ˣ, (ℤ/62720)ˣ, (ℤ/62860)ˣ, (ℤ/64656)ˣ, (ℤ/66816)ˣ, (ℤ/67164)ˣ, (ℤ/70044)ˣ, (ℤ/80820)ˣ, (ℤ/94290)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C32 | C24×C3×C7 |
| socle, prime radical | C24×C3×C7 | C2×C32 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
3092 conjugacy classes of subgroups.
21504 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.