Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Fitting | C7×#102 ⋊ C2 |
| Sylow | C7 ⋊ #490 |
110 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 110 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) = 224 |
A minimal faithful permutation representation — 3 generators on 23 points:
(1,2,4,6,7,5,3)(8,10,11,15)(9,13,12,14)(16,17)(18,23)(19,20)(21,22);(9,12)(13,14)(17,21)(18,22)(20,23);(2,3)(4,5)(6,7)(8,9,11,12)(10,14,15,13)(17,20)(21,23)Polycyclic presentation:
2^6,7|a^2=e,c^2=e,d^2=f,b^a=be,c^a=cef,g^a=g^6,c^b=cd,d^b=df,d^c=df58 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#89536, #11736182, #11736207, … |
| maximal normal subgroup of | C2×#89536, #11736182, #11736207, … |
| maximal quotient of | #11726559, #11726565, #11726597, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 298);