Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C7×#106 ⋊ C2 |
| Sylow | C7 ⋊ C4×SD16 |
122 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 122 conjugacy classes of subgroups — too many to draw. Only its 51 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)(8,10,11,9)(12,13,15,17)(14,19,18,16);(8,9,11,10)(13,16)(14,18)(17,19);(2,3)(4,5)(6,7)(8,9,11,10)Polycyclic presentation:
2^6,7|a^2=e,b^2=e,c^2=ef,d^2=f,g^a=g^6,c^b=cd,d^b=df,d^c=df70 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#89624, #11736551, #11736569, … |
| maximal normal subgroup of | C2×#89624, #11736551, #11736569, … |
| maximal quotient of | #11726270, #11726273, #11726274, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 386);