Finite Group DatabasebetaFinite Group Databasebeta| order | 18816 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 516096 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C2×C7 |
| abelian | C2×C3×C72×C64 |
| multiplicative | (ℤ/19307)ˣ, (ℤ/22001)ˣ, (ℤ/38614)ˣ, (ℤ/44002)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C32 | C22×C3×C72 |
| socle, prime radical | C22×C3×C72 | C32 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
400 conjugacy classes of subgroups.
18816 conjugacy classes. The character table is too large to display.
| automorphism group of | C43×C449 |
| outer automorphism group of | C43×C449 |
Past the SmallGroups library coverage — no SmallGroups id.