Finite Group DatabasebetaFinite Group Databasebeta| order | 26520 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 12288 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C2 |
| abelian | C2×C3×C4×C5×C13×C17 |
| multiplicative | (ℤ/27023)ˣ, (ℤ/30947)ˣ, (ℤ/33175)ˣ, (ℤ/39789)ˣ, (ℤ/54046)ˣ, (ℤ/61894)ˣ, (ℤ/66350)ˣ, (ℤ/79578)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2 | C22×C3×C5×C13×C17 |
| socle, prime radical | C22×C3×C5×C13×C17 | C2 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
128 conjugacy classes of subgroups.
26520 conjugacy classes. The character table is too large to display.
| automorphism group of | C61×C443 |
| outer automorphism group of | C61×C443 |
Past the SmallGroups library coverage — no SmallGroups id.