Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C4×D4×D7 |
| Fitting | C4×C7×D4 ⋊ C2 |
| Sylow | C7 ⋊ C2×C4×D4 |
426 conjugacy classes of subgroups; only the 169 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 169 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 15 |
| transitive degree | μt(G) = 112 |
A minimal faithful permutation representation — 4 generators on 15 points:
(2,3)(4,5)(6,7);(1,2,4,6,7,5,3)(13,15);(12,13)(14,15);(8,9,10,11)100 conjugacy classes — view the full character table.
| maximal subgroup of | D7×D4⋊C8, #11725921, #11725926, … |
| maximal normal subgroup of | D7×D4⋊C8, #11725921, #11725926, … |
| maximal quotient of | C4×(C22⋊D7)⋊C4, C4×#6441, C4×#6448, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 997);