Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C7×#104 ⋊ C2 |
| Sylow | C7 ⋊ #421 |
154 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 51 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)(8,11,12,10,13,18,21,19)(9,15,16,22,17,20,23,14);(8,10)(9,14)(11,21)(12,18)(13,19)(15,16)(17,22)(20,23);(2,3)(4,5)(6,7)(8,9)(10,14)(11,20)(12,16)(13,17)(15,18)(19,22)(21,23)Polycyclic presentation:
2^6,7|c^2=d,d^2=f,e^2=f,c^a=cf,g^a=g^6,c^b=ce,e^b=ef,e^c=ef64 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#89593, #11736428, D7×#421, … |
| maximal normal subgroup of | C2×#89593, #11736428, D7×#421, … |
| maximal quotient of | #11725920, #11725921, #11725922, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 355);