Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C7×C4⋊Q8 ⋊ C2 |
| Sylow | C7 ⋊ #492 |
142 conjugacy classes of subgroups.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 224 |
A minimal faithful permutation representation — 3 generators on 19 points:
(1,2,4,6,7,5,3)(9,11)(12,13,15,17)(14,19,18,16);(8,9,10,11);(2,3)(4,5)(6,7)(9,11)(13,16)(14,18)(17,19)Polycyclic presentation:
2^6,7|b^2=e,c^2=f,d^2=f,b^a=be,c^a=cd,d^a=df,g^a=g^6,c^b=ce,d^c=df64 conjugacy classes — view the full character table.
| maximal subgroup of | #11725358, #11726194, #11726202, … |
| maximal normal subgroup of | #11725358, #11726194, #11726202, … |
| maximal quotient of | #11727330, #11727334, #11727341, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 619);