Finite Group DatabasebetaFinite Group Databasebeta| order | 22800 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 348364800 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C26×C5 |
| abelian | C24×C3×C52×C19 |
| multiplicative | (ℤ/44121)ˣ, (ℤ/47368)ˣ, (ℤ/50248)ˣ, (ℤ/58828)ˣ, (ℤ/71052)ˣ, (ℤ/75372)ˣ, (ℤ/75636)ˣ, (ℤ/88242)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator, Frattini | C1 | G |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
2144 conjugacy classes of subgroups.
22800 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.