Finite Group DatabasebetaFinite Group Databasebeta| order | 22800 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 276480 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C2×C5 |
| abelian | C2×C3×C52×C8×C19 |
| multiplicative | (ℤ/23411)ˣ, (ℤ/23591)ˣ, (ℤ/25091)ˣ, (ℤ/46822)ˣ, (ℤ/47182)ˣ, (ℤ/50182)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C4 | C22×C3×C52×C19 |
| socle, prime radical | C22×C3×C52×C19 | C4 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
352 conjugacy classes of subgroups.
22800 conjugacy classes. The character table is too large to display.
| automorphism group of | C41×C571, C31×C761 |
| outer automorphism group of | C41×C571, C31×C761 |
Past the SmallGroups library coverage — no SmallGroups id.