Finite Group DatabasebetaFinite Group Databasebeta| order | 1248 |
| isoclinism | isoclinic class of #6118 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C8 · Schur multiplier (H2) = C2 |
| direct product | C3×C4⋊#1057 |
| unambiguous semidirect product | C4⋊(C3×#1057) |
| Hall | C3×C13 ⋊ C4⋊C8 |
| Sylow | C13 ⋊ C3×C4⋊C8 |
76 conjugacy classes of subgroups.
| minimal degree | μ(G) = 28 |
| transitive degree | μt(G) = 1248 |
A minimal faithful permutation representation — 2 generators on 28 points:
(1,2,3)(4,5,8,11,15,9,13,14,6,10,16,12,7)(17,18,19,20);(5,6,7,9)(8,11,12,16)(10,14,15,13)(18,20)(21,22,23,25,24,26,27,28)132 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1248, 460);