Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | (C22⋊D7)⋊C8 |
| Fitting | C7×C22⋊C8 ⋊ C2 |
| Sylow | C7 ⋊ C8×D4 |
134 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 134 conjugacy classes of subgroups — too many to draw. Only its 61 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:
(1,2,4,6,7,5,3)(9,11)(12,13,14,16,15,17,18,19);(8,9)(10,11);(2,3)(4,5)(6,7)(9,11)Polycyclic presentation:
2^6,7|c^2=d,d^2=f,b^a=be,g^a=g^6,c^b=ce100 conjugacy classes — view the full character table.
| maximal subgroup of | C2×(C22⋊D7)⋊C8, #11736041, #11736046, … |
| maximal normal subgroup of | C2×(C22⋊D7)⋊C8, #11736041, #11736046, … |
| maximal quotient of | #11725902, #11725903, #11725904, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 259);