Finite Group DatabasebetaFinite Group Databasebeta| order | 1456 |
| isoclinism | isoclinic class of #1132 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C13 · Schur multiplier (H2) = C1 |
| direct product | C13×#1132 |
| Fitting | C7×C8×C13 ⋊ C2 |
| Hall | C7×C13 ⋊ SD16 |
| Sylow | C7 ⋊ C13×SD16 |
40 conjugacy classes of subgroups.
| minimal degree | μ(G) = 28 |
| transitive degree | μt(G) = 728 |
A minimal faithful permutation representation — 2 generators on 28 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,17,19,20,18,16)(21,22,23,25,24,26,27,28);(15,16)(17,18)(19,20)(22,25)(23,27)(26,28)403 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1456, 50);