Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C7×#101 ⋊ C2 |
| Sylow | C7 ⋊ #473 |
100 conjugacy classes of subgroups; only the 35 normal subgroups are shown.
This group has 100 conjugacy classes of subgroups — too many to draw. Only its 35 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 224 |
A minimal faithful permutation representation — 3 generators on 39 points:
(1,2,4,6,7,5,3)(8,11,13,24)(9,15,17,30)(10,18,20,22)(12,25,26,23)(14,27,29,38)(16,31,32,21)(19,35,36,34)(28,33,39,37);(8,10,12,19,13,20,26,36)(9,14,16,28,17,29,32,39)(11,22,23,35,24,18,25,34)(15,27,21,37,30,38,31,33);(2,3)(4,5)(6,7)(8,9)(10,14)(11,21)(12,16)(13,17)(15,25)(18,33)(19,28)(20,29)(22,37)(23,30)(24,31)(26,32)(27,34)(35,38)(36,39)Polycyclic presentation:
2^6,7|b^2=d,c^2=f,d^2=f,c^a=cde,e^a=ef,g^a=g^6,c^b=cef,e^b=ef,d^c=df49 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#89527, #11736157, #11736164, … |
| maximal normal subgroup of | C2×#89527, #11736157, #11736164, … |
| maximal quotient of | #11726195, #11726197, #11726198, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 289);