Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C7×#108 ⋊ 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)(8,11,12,21,13,22,23,14)(9,15,16,20,18,10,17,19);(8,10,12,19,13,15,23,20)(9,14,17,22,18,21,16,11);(2,3)(4,5)(6,7)(8,9)(10,14)(11,20)(12,17)(13,18)(15,21)(16,23)(19,22)Polycyclic presentation:
2^6,7|b^2=e,c^2=d,d^2=f,e^2=f,c^a=cd,d^a=df,g^a=g^6,c^b=cef,e^c=ef58 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#89670, #11736701, #11736706, … |
| maximal normal subgroup of | C2×#89670, #11736701, #11736706, … |
| maximal quotient of | #11726290, #11726291, #11726298, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 432);