Finite Group DatabasebetaFinite Group Databasebeta| order | 1404 |
| isoclinism | isoclinic class of C9⋊A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C13 · Schur multiplier (H2) = C2×C32 |
| direct product | C13×C22⋊H(3,𝔽3) |
| unambiguous semidirect product | C22⋊(C13×H(3,𝔽3)) |
| unambiguous semidirect product | C32⋊(A4×C13) |
| unambiguous semidirect product | (C3×A4)⋊(C3×C13) |
| Fitting | C22×C32×C13 ⋊ C3 |
| Hall | C22×C13 ⋊ H(3,𝔽3) |
| Sylow | C22 ⋊ C13×H(3,𝔽3) |
56 conjugacy classes of subgroups.
| minimal degree | μ(G) = 26 |
| transitive degree | μt(G) = 234 |
A minimal faithful permutation representation — 2 generators on 26 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,17)(15,16)(19,22,23)(21,25,26);(15,16,17)(18,19,21)(20,23,25)(22,26,24)260 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1404, 135);