Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C7×M32 ⋊ 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)(8,10,18,9,13,20,11,15,14,21,17,16,12,23,22,19);(2,3)(4,5)(6,7)(8,9)(10,17)(11,20)(12,15)(13,19)(14,16)(18,21)(22,23)Polycyclic presentation:
2^6,7|b^2=cd,c^2=ef,d^2=f,e^2=f,b^a=bc,c^a=ce,e^a=ef,g^a=g^6,c^b=cf,d^b=df76 conjugacy classes — view the full character table.
| maximal subgroup of | #11726844, #11726845, #11726874, … |
| maximal normal subgroup of | #11726844, #11726845, #11726874, … |
| maximal quotient of | #11725322, #11725323, #11725332, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 75);