Finite Group DatabasebetaFinite Group Databasebeta| order | 1248 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23 |
| direct product | C4×D4×C13⋊C3 |
| unambiguous semidirect product | (C4×D4×C13)⋊C3 |
| Fitting, Hall | C4×D4×C13 ⋊ C3 |
| Sylow | C13 ⋊ C3×C4×D4 |
188 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 96 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 208 |
A minimal faithful permutation representation — 3 generators on 21 points:
(1,2,3,4)(10,11,13)(12,15,18)(14,17,16)(19,21,20);(5,6,7,8)(9,10,12,11,14,18,15,19,21,13,16,20,17);(6,8)140 conjugacy classes — view the full character table.
| maximal subgroup of | C4×D4×D13⋊C3, C13⋊C3×#442, #72276135 |
| maximal normal subgroup of | C4×D4×D13⋊C3, C13⋊C3×#442, #72276135 |
| maximal quotient of | C13⋊C3×#442 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1248, 835);