Finite Group DatabasebetaFinite Group Databasebeta| order | 1080 |
| isoclinism | isoclinic class of D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C8×C27 · Schur multiplier (H2) = C1 |
| direct product | C27×#168 |
| derived, Sylow | C5 ⋊ C8×C27 |
| Hall | C5×C27 ⋊ C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4×C27 | D5 |
| commutator, hypocenter | C5 | C8×C27 |
| Frattini | C4×C9 | C3×D5 |
| Fitting | C4×C5×C27 | C2 |
| socle, prime radical | C2×C3×C5 | C4×C9 |
| cosocle | C4×C5×C9 | C2×C3 |
| LCS | G ▷ C5 | |
| UCS | C1 ◁ C4×C27 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1080 |
432 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1080, 2);