Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×C7×M16 ⋊ C2 |
| Sylow | C7 ⋊ #413 |
150 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 150 conjugacy classes of subgroups — too many to draw. Only its 59 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)(8,11,12,19,13,20,10,17)(9,15,14,22,16,18,21,23);(8,10,13,12)(9,14,16,21)(11,17,20,19)(15,22,18,23);(2,3)(4,5)(6,7)(8,9)(10,14)(11,18)(12,21)(13,16)(15,20)(17,23)(19,22)Polycyclic presentation:
2^6,7|b^2=f,c^2=d,d^2=f,c^a=ce,d^a=df,g^a=g^6,e^c=ef82 conjugacy classes — view the full character table.
| maximal subgroup of | #11726454, #11726465, #11726473, … |
| maximal normal subgroup of | #11726454, #11726465, #11726473, … |
| maximal quotient of | #11727551, #11727553, #11727612, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 666);