Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C7×C22⋊C8 ⋊ C2 |
| Sylow | C7 ⋊ #448 |
158 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)(12,14,15,13,16,17,19,18);(8,9)(10,11);(2,3)(4,5)(6,7)(12,13,16,18)(14,19,17,15)Polycyclic presentation:
2^6,7|a^2=f,c^2=d,d^2=f,c^a=cd,d^a=df,g^a=g^6,c^b=ce79 conjugacy classes — view the full character table.
| maximal subgroup of | #11725862, #11725863, #11725886, … |
| maximal normal subgroup of | #11725862, #11725863, #11725886, … |
| maximal quotient of | #11725868, #11725870, #11725892, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 272);