Finite Group DatabasebetaFinite Group Databasebeta| order | 27040 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 79872 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C4 |
| abelian | C4×C5×C8×C169 |
| multiplicative | (ℤ/27757)ˣ, (ℤ/33805)ˣ, (ℤ/55514)ˣ, (ℤ/67610)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C4×C13 | C22×C5×C13 |
| socle, prime radical | C22×C5×C13 | C2×C4×C13 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
132 conjugacy classes of subgroups.
27040 conjugacy classes. The character table is too large to display.
| automorphism group of | C41×C677 |
| outer automorphism group of | C41×C677 |
Past the SmallGroups library coverage — no SmallGroups id.