Finite Group DatabasebetaFinite Group Databasebeta| order | 21720 |
| 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×C5×C181 |
| multiplicative | (ℤ/23543)ˣ, (ℤ/27155)ˣ, (ℤ/27175)ˣ, (ℤ/32583)ˣ, (ℤ/43444)ˣ, (ℤ/47086)ˣ, (ℤ/54310)ˣ, (ℤ/54350)ˣ, (ℤ/65166)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2 | C22×C3×C5×C181 |
| socle, prime radical | C22×C3×C5×C181 | C2 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
64 conjugacy classes of subgroups.
21720 conjugacy classes. The character table is too large to display.
| automorphism group of | C13×C1811 |
| outer automorphism group of | C13×C1811 |
Past the SmallGroups library coverage — no SmallGroups id.