Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×D4×Dic7 |
| Sylow | C7 ⋊ C2×C4×D4 |
426 conjugacy classes of subgroups; only the 215 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 215 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 17 |
| transitive degree | μt(G) = 224 |
A minimal faithful permutation representation — 4 generators on 17 points:
(3,4,5,6)(12,13)(14,15)(16,17);(1,2)(7,8)(9,10)(11,12,14,16,17,15,13);(1,2)(8,10);(1,2)100 conjugacy classes — view the full character table.
| maximal subgroup of | Dic7×#99, #11727782, Dic7×#100, … |
| maximal normal subgroup of | Dic7×#99, #11727782, Dic7×#100, … |
| maximal quotient of | C2×C22⋊C4×Dic7, C2×#89722, C2×#89723, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 1248);