Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C7×#97 ⋊ C2 |
| Sylow | C7 ⋊ C4×M16 |
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)(12,13,14,17,15,16,18,19);(8,9,10,11)(13,16)(17,19);(2,3)(4,5)(6,7)(13,16)(17,19)Polycyclic presentation:
2^6,7|b^2=e,c^2=d,d^2=f,c^a=cf,g^a=g^6,c^b=cf100 conjugacy classes — view the full character table.
| maximal subgroup of | #11726095, #11726096, #11726097, … |
| maximal normal subgroup of | #11726095, #11726096, #11726097, … |
| maximal quotient of | #11725821, #11725824, #11725826, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 241);