Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×C7×SD16 ⋊ C2 |
| Sylow | C7 ⋊ #471 |
104 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 104 conjugacy classes of subgroups — too many to draw. Only its 37 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)(9,14)(10,17)(11,19)(13,20)(15,16)(18,23);(8,10,11,17,12,18,19,23)(9,13,14,22,16,20,15,21);(2,3)(4,5)(6,7)(8,9)(10,13)(11,14)(12,16)(15,19)(17,22)(18,20)(21,23)Polycyclic presentation:
2^6,7|b^2=e,d^2=f,e^2=f,c^a=cd,d^a=df,g^a=g^6,c^b=cef,d^c=df,e^c=ef58 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#471, #11738374, #11738375, … |
| maximal normal subgroup of | D7×#471, #11738374, #11738375, … |
| maximal quotient of | #11727949, #11727950, #11727951, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 711);