Finite Group DatabasebetaFinite Group Databasebeta| order | 18288 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 72576 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C4 |
| abelian | C42×C9×C127 |
| multiplicative | (ℤ/18833)ˣ, (ℤ/37666)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C22×C3 | C22×C3×C127 |
| socle, prime radical | C22×C3×C127 | C22×C3 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
90 conjugacy classes of subgroups.
18288 conjugacy classes. The character table is too large to display.
| automorphism group of | C37×C509 |
| outer automorphism group of | C37×C509 |
Past the SmallGroups library coverage — no SmallGroups id.