Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C7×C22⋊C8 ⋊ C2 |
| Sylow | C7 ⋊ #480 |
114 conjugacy classes of subgroups.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 224 |
A minimal faithful permutation representation — 3 generators on 23 points:
(1,2,4,6,7,5,3)(9,13)(10,15)(16,17,21,23,19,22,18,20);(8,10)(9,12)(11,15)(13,14);(2,3)(4,5)(6,7)(8,9)(10,14)(11,13)(12,15)(17,20)(18,21)(22,23)Polycyclic presentation:
2^6,7|c^2=def,d^2=f,b^a=be,c^a=cd,d^a=df,g^a=g^6,c^b=ce79 conjugacy classes — view the full character table.
| maximal subgroup of | #11725864, #11725865, #11725888, … |
| maximal normal subgroup of | #11725864, #11725865, #11725888, … |
| maximal quotient of | #11726375, #11726379, #11726389, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 270);