Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4 |
| direct product | C22⋊C4×Dic7 |
| Sylow | C7 ⋊ C4×C22⋊C4 |
258 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 111 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) = 224 |
A minimal faithful permutation representation — 3 generators on 19 points:
(2,3)(4,5)(6,7)(12,13,14,15);(1,2,4,6,7,5,3)(17,19);(8,9,10,11)(16,17)(18,19)100 conjugacy classes — view the full character table.
| maximal subgroup of | #11726706, #11726709, Dic7×#99, … |
| maximal normal subgroup of | #11726706, #11726709, Dic7×#99, … |
| maximal quotient of | Dic7×#95, #11727155, #11727161, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 475);