Finite Group DatabasebetaFinite Group Databasebeta| order | 22920 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 255360 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23 |
| abelian | C23×C3×C5×C191 |
| multiplicative | (ℤ/29491)ˣ, (ℤ/35619)ˣ, (ℤ/37917)ˣ, (ℤ/47492)ˣ, (ℤ/58982)ˣ, (ℤ/71238)ˣ, (ℤ/75834)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator, Frattini | C1 | G |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
128 conjugacy classes of subgroups.
22920 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.