Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C7×AGL(1,ℤ/8) ⋊ C2 |
| Sylow | C7 ⋊ #454 |
146 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 146 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) = 112 |
A minimal faithful permutation representation — 3 generators on 23 points:
(1,2,4,6,7,5,3)(9,15)(10,18)(11,12)(16,17)(19,20)(21,22);(8,10,13,20)(9,14,17,23)(11,19,12,18)(15,22,16,21);(2,3)(4,5)(6,7)(8,9)(10,14)(11,15)(12,16)(13,17)(18,21)(19,22)(20,23)Polycyclic presentation:
2^6,7|b^2=f,d^2=f,e^2=f,c^a=cd,d^a=df,g^a=g^6,c^b=ce,e^b=ef,d^c=df,e^c=ef49 conjugacy classes — view the full character table.
| maximal subgroup of | #11737722, #11737724, D7×#454, … |
| maximal normal subgroup of | #11737722, #11737724, D7×#454, … |
| maximal quotient of | #11728052, #11728062, #11728063, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 735);