Finite Group DatabasebetaFinite Group Databasebeta| order | 18400 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 14080 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C2 |
| abelian | C2×C16×C23×C25 |
| multiplicative | (ℤ/18847)ˣ, (ℤ/19567)ˣ, (ℤ/37694)ˣ, (ℤ/39134)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C5×C8 | C22×C5×C23 |
| socle, prime radical | C22×C5×C23 | C5×C8 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
84 conjugacy classes of subgroups.
18400 conjugacy classes. The character table is too large to display.
| automorphism group of | C47×C401, C17×C1151 |
| outer automorphism group of | C47×C401, C17×C1151 |
Past the SmallGroups library coverage — no SmallGroups id.