Finite Group DatabasebetaFinite Group Databasebeta| order | 22200 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 11520 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C2 |
| abelian | C2×C3×C4×C25×C37 |
| multiplicative | (ℤ/22499)ˣ, (ℤ/22523)ˣ, (ℤ/25907)ˣ, (ℤ/27875)ˣ, (ℤ/33309)ˣ, (ℤ/44998)ˣ, (ℤ/45046)ˣ, (ℤ/51814)ˣ, (ℤ/55750)ˣ, (ℤ/66618)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C5 | C22×C3×C5×C37 |
| socle, prime radical | C22×C3×C5×C37 | C2×C5 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
96 conjugacy classes of subgroups.
22200 conjugacy classes. The character table is too large to display.
| automorphism group of | C149×C151, C101×C223 |
| outer automorphism group of | C149×C151, C101×C223 |
Past the SmallGroups library coverage — no SmallGroups id.