Finite Group DatabasebetaFinite Group Databasebeta| order | 17496 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 69984 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C2×C3 |
| abelian | C2×C3×C4×C729 |
| multiplicative | (ℤ/18967)ˣ, (ℤ/20419)ˣ, (ℤ/26253)ˣ, (ℤ/28431)ˣ, (ℤ/37934)ˣ, (ℤ/40838)ˣ, (ℤ/52506)ˣ, (ℤ/56862)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C243 | C22×C32 |
| socle, prime radical | C22×C32 | C2×C243 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
208 conjugacy classes of subgroups.
17496 conjugacy classes. The character table is too large to display.
| automorphism group of | C13×C1459, C7×C2917, C13×C2187 |
| outer automorphism group of | C13×C1459, C7×C2917, C13×C2187 |
Past the SmallGroups library coverage — no SmallGroups id.