Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C7×#99 ⋊ C2 |
| Sylow | C7 ⋊ AΣL(1,𝔽16) |
94 conjugacy classes of subgroups.
| minimal degree | μ(G) = 15 |
| transitive degree | μt(G) = 56 |
A minimal faithful permutation representation — 2 generators on 15 points:
(1,2,4,6,7,5,3)(8,9)(10,14,15,12)(11,13);(2,3)(4,5)(6,7)(9,12)(13,14)Polycyclic presentation:
2^6,7|b^2=c,b^a=bd,c^a=ce,g^a=g^6,d^b=de,e^b=ef,d^c=df46 conjugacy classes — view the full character table.
| maximal subgroup of | D7×AΣL(1,𝔽16), #11726891, #11726897, … |
| maximal normal subgroup of | D7×AΣL(1,𝔽16), #11726891, #11726897, … |
| maximal quotient of | #11725250, #11725252, #11725262, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 28);