Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Fitting | C7×C22⋊C8 ⋊ C2 |
| Sylow | C7 ⋊ #482 |
106 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 106 conjugacy classes of subgroups — too many to draw. Only its 39 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 224 |
A minimal faithful permutation representation — 3 generators on 23 points:
(1,2,4,6,7,5,3)(9,13)(10,15)(16,17,18,20,19,21,22,23);(8,10)(9,12)(11,15)(13,14)(17,21)(20,23);(2,3)(4,5)(6,7)(8,9)(10,14)(11,13)(12,15)(17,20)(18,22)(21,23)Polycyclic presentation:
2^6,7|c^2=de,d^2=f,b^a=be,c^a=cd,d^a=df,g^a=g^6,c^b=cef79 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#89509, #11736036, #11736058, … |
| maximal normal subgroup of | C2×#89509, #11736036, #11736058, … |
| maximal quotient of | #11726377, #11726378, #11726379, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 271);