Finite Group DatabasebetaFinite Group Databasebeta| order | 10752 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 196608 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C22×C4 |
| abelian | C2×C3×C4×C7×C64 |
| multiplicative | (ℤ/15715)ˣ, (ℤ/16791)ˣ, (ℤ/17511)ˣ, (ℤ/20205)ˣ, (ℤ/22388)ˣ, (ℤ/23348)ˣ, (ℤ/31430)ˣ, (ℤ/33582)ˣ, (ℤ/35022)ˣ, (ℤ/40410)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C32 | C23×C3×C7 |
| socle, prime radical | C23×C3×C7 | C2×C32 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
648 conjugacy classes of subgroups.
10752 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.