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 ⋊ #575 |
262 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 262 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)(9,14)(10,17)(11,19)(13,21)(16,18)(20,23);(8,10)(9,13)(11,17)(12,16)(14,20)(15,23)(18,19)(21,22);(10,16)(13,20)(17,18)(21,23);(2,3)(4,5)(6,7)(8,9)(10,13)(11,15)(12,14)(16,20)(17,23)(18,21)(19,22)Polycyclic presentation:
2^6,7|e^2=f,d^a=df,g^a=g^6,c^b=cf,d^c=de,e^c=ef,e^d=ef55 conjugacy classes — view the full character table.
| maximal subgroup of | #11737722, #11737723, #11737729, … |
| maximal normal subgroup of | #11737722, #11737723, #11737729, … |
| maximal quotient of | #11736312, #11736316, #11736324, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 1226);