Finite Group DatabasebetaFinite Group Databasebeta| order | 360 |
| isoclinism | isoclinic class of D3 |
| automorphism | Aut(G) = C23×C4×D3 (order 192) · Inn(G) = D3 · Out(G) = C23×C4 |
| homology | Abelianization (H1) = C2×C3×C4×C5 · Schur multiplier (H2) = C2 |
| direct product | C3×C4×C5×D3 |
| Fitting | C32×C4×C5 ⋊ C2 |
| derived | C3 ⋊ C2×C3×C4×C5 |
| Hall | C32×C5 ⋊ C2×C4 |
| Sylow | C32 ⋊ C2×C4×C5 |
70 conjugacy classes of subgroups.
| minimal degree | μ(G) = 15 |
| transitive degree | μt(G) = 120 |
A minimal faithful permutation representation — 2 generators on 15 points:
(1,2,3)(5,6)(7,8,9,10,11);(4,5,6)(12,15,14,13)180 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(360, 96);