Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4 |
| direct product | D7×#117 |
| Fitting | C7×#117 ⋊ C2 |
| Sylow | C7 ⋊ C2×#117 |
330 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 159 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 112 |
A minimal faithful permutation representation — 4 generators on 19 points:
(5,7,8,11)(6,10,9,12)(13,14,16,18,19,17,15);(6,9)(10,12);(1,2,3,4)(5,6)(7,10)(8,9)(11,12);(14,15)(16,17)(18,19)100 conjugacy classes — view the full character table.
| maximal subgroup of | D7×H(3,ℤ/4), D7×#339, #11726507, … |
| maximal normal subgroup of | D7×H(3,ℤ/4), D7×#339, #11726507, … |
| maximal quotient of | #11730827, #11730829, #11730837, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 973);