Finite Group DatabasebetaFinite Group Databasebeta| order | 1248 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C2×C4 |
| direct product | C13×#892 |
| Fitting | C3×C13×C4⋊C4 ⋊ C2 |
| Hall | C3×C13 ⋊ #117 |
| Sylow | C3 ⋊ C13×#117 |
152 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 82 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 28 |
| transitive degree | μt(G) = 624 |
A minimal faithful permutation representation — 3 generators on 28 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,16)(17,18,19,20)(22,26)(23,27);(21,23,24,27)(22,25,26,28);(15,16)(21,22)(23,25)(24,26)(27,28)390 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1248, 981);