Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| isoclinism | isoclinic class of #89246 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C7×#97 ⋊ C2 |
| Sylow | C7 ⋊ #329 |
70 conjugacy classes of subgroups.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 224 |
A minimal faithful permutation representation — 2 generators on 23 points:
(1,2,4,6,7,5,3)(8,9,10,13,11,12,14,15)(17,20,21,22);(2,3)(4,5)(6,7)(9,12)(10,14)(16,17)(18,20)(19,21)(22,23)Polycyclic presentation:
2^6,7|b^2=c,c^2=f,d^2=ef,b^a=bd,c^a=ce,d^a=def,g^a=g^6,d^b=df79 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#329, #11726096, #11726097, … |
| maximal normal subgroup of | D7×#329, #11726096, #11726097, … |
| maximal quotient of | #11725285, #11725286, #11725326, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 21);