Finite Group DatabasebetaFinite Group Databasebeta| order | 1080 |
| isoclinism | isoclinic class of #1201 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C3 |
| direct product | C32×#1204 |
| Hall | C33×C5 ⋊ Q8 |
| Sylow | C33 ⋊ Dic10 |
| Sylow | C5 ⋊ C32×Dic6 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C32 | D3×D5 |
| commutator, cosocle | C2×C3×C5 | C22×C32 |
| Frattini | C2 | C32×D3×D5 |
| Fitting, socle, prime radical | C2×C33×C5 | C22 |
| hypocenter | C3×C5 | C32×Q8 |
| LCS | G ▷ C2×C3×C5 ▷ C3×C5 | |
| UCS | C1 ◁ C2×C32 | |
192 conjugacy classes of subgroups.
| transitive degree | μt(G) = 360 |
189 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1080, 380);