Finite Group DatabasebetaFinite Group Databasebeta| order | 288 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3 |
| direct product | C3×Q8×A4 |
| Fitting | C22×C3×Q8 ⋊ C3 |
| Sylow | C22×Q8 ⋊ C32 |
116 conjugacy classes of subgroups.
| minimal degree | μ(G) = 15 |
| transitive degree | μt(G) = 72 |
A minimal faithful permutation representation — 2 generators on 15 points:
(2,3,4)(5,12,8,7)(6,11,10,9);(1,4)(2,3)(5,10,8,6)(7,9,12,11)(13,14,15)60 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(288, 982);