Finite Group DatabasebetaFinite Group Databasebeta| order | 27160 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 18432 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C2 |
| abelian | C2×C4×C5×C7×C97 |
| multiplicative | (ℤ/27619)ˣ, (ℤ/28159)ˣ, (ℤ/33955)ˣ, (ℤ/55238)ˣ, (ℤ/56318)ˣ, (ℤ/67910)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2 | C22×C5×C7×C97 |
| socle, prime radical | C22×C5×C7×C97 | C2 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
64 conjugacy classes of subgroups.
27160 conjugacy classes. The character table is too large to display.
| automorphism group of | C71×C389 |
| outer automorphism group of | C71×C389 |
Past the SmallGroups library coverage — no SmallGroups id.