Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C2×C7×C22⋊C4 ⋊ C2 |
| Sylow | C7 ⋊ #390 |
258 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 77 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)(8,9,10,11)(16,17)(18,19);(13,15)(17,19);(2,3)(4,5)(6,7)(12,13)(14,15)(17,19)Polycyclic presentation:
2^6,7|c^2=d,b^a=be,c^a=cf,g^a=g^6,c^b=cf88 conjugacy classes — view the full character table.
| maximal subgroup of | #11730884, C4×#6448, #11730894, … |
| maximal normal subgroup of | #11730884, C4×#6448, #11730894, … |
| maximal quotient of | Dic7⋊#95, #11727162, #11727175, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 491);