Finite Group DatabasebetaFinite Group Databasebeta| order | 1512 |
| isoclinism | isoclinic class of Dic14 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C27 · Schur multiplier (H2) = C2 |
| direct product | C27×C22⋊D7 |
| Fitting | C22×C7×C27 ⋊ C2 |
| Hall | C7×C27 ⋊ D4 |
| Sylow | C7 ⋊ D4×C27 |
64 conjugacy classes of subgroups.
| minimal degree | μ(G) = 38 |
| transitive degree | μt(G) = 756 |
A minimal faithful permutation representation — 2 generators on 38 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27)(28,29,31,33,34,32,30)(36,38);(29,30)(31,32)(33,34)(35,36)(37,38)459 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1512, 28);