Finite Group DatabasebetaFinite Group Databasebeta| order | 23680 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 294912 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C8 |
| abelian | C5×C8×C16×C37 |
| multiplicative | (ℤ/24313)ˣ, (ℤ/25177)ˣ, (ℤ/48626)ˣ, (ℤ/50354)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C4×C8 | C22×C5×C37 |
| socle, prime radical | C22×C5×C37 | C4×C8 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
208 conjugacy classes of subgroups.
23680 conjugacy classes. The character table is too large to display.
| automorphism group of | C41×C593, C17×C1481 |
| outer automorphism group of | C41×C593, C17×C1481 |
Past the SmallGroups library coverage — no SmallGroups id.