Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×C7×#41 ⋊ C2 |
| Sylow | C7 ⋊ #449 |
162 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 47 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)(12,14,15,16)(13,17,18,19);(12,13)(14,17)(15,18)(16,19);(2,3)(4,5)(6,7)(8,9)(10,11)(13,17)(14,16)(18,19)Polycyclic presentation:
2^6,7|c^2=f,e^2=f,b^a=be,c^a=cd,e^a=ef,g^a=g^6,e^b=ef79 conjugacy classes — view the full character table.
| maximal subgroup of | #11736291, #11736293, #11736295, … |
| maximal normal subgroup of | #11736291, #11736293, #11736295, … |
| maximal quotient of | #11729330, #11729340, #11729361, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 772);