Finite Group DatabasebetaFinite Group Databasebeta| order | 22920 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 12160 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C2 |
| abelian | C2×C3×C4×C5×C191 |
| multiplicative | (ℤ/23363)ˣ, (ℤ/25223)ˣ, (ℤ/26747)ˣ, (ℤ/34389)ˣ, (ℤ/46726)ˣ, (ℤ/50446)ˣ, (ℤ/53494)ˣ, (ℤ/68778)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2 | C22×C3×C5×C191 |
| socle, prime radical | C22×C3×C5×C191 | C2 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
64 conjugacy classes of subgroups.
22920 conjugacy classes. The character table is too large to display.
| automorphism group of | C61×C383 |
| outer automorphism group of | C61×C383 |
Past the SmallGroups library coverage — no SmallGroups id.