Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C7×#106 ⋊ C2 |
| Sylow | C7 ⋊ #360 |
58 conjugacy classes of subgroups.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 112 |
A minimal faithful permutation representation — 2 generators on 23 points:
(1,2,4,6,7,5,3)(9,13,14,22)(10,17)(11,18)(15,21,23,16)(19,20);(2,3)(4,5)(6,7)(8,9)(10,13)(11,21)(12,14)(15,19)(16,18)(17,23)(20,22)Polycyclic presentation:
2^6,7|b^2=c,d^2=ef,e^2=f,b^a=bd,c^a=cf,d^a=de,e^a=ef,g^a=g^6,d^b=def,e^b=ef58 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#360, #11727005, #11727006, … |
| maximal normal subgroup of | D7×#360, #11727005, #11727006, … |
| maximal quotient of | #11725271, #11725272, #11725273, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 45);