Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C7×AGL(1,ℤ/8) ⋊ C2 |
| Sylow | C7 ⋊ #576 |
268 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 99 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 — 4 generators on 23 points:
(1,2,4,6,7,5,3)(8,10)(9,14)(11,19)(12,16)(13,20)(15,23)(17,18)(21,22);(10,17)(11,18)(14,22)(15,21)(16,19)(20,23);(9,13)(10,16)(15,21)(17,19);(2,3)(4,5)(6,7)(8,9)(10,14)(11,15)(12,13)(16,20)(17,22)(18,21)(19,23)Polycyclic presentation:
2^6,7|e^2=f,b^a=bf,g^a=g^6,d^b=df,d^c=de,e^c=ef,e^d=ef55 conjugacy classes — view the full character table.
| maximal subgroup of | #11737725, #11737727, #11737732, … |
| maximal normal subgroup of | #11737725, #11737727, #11737732, … |
| maximal quotient of | #11736313, #11736317, #11736319, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 1227);