Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C7×#99 ⋊ C2 |
| Sylow | C7 ⋊ #353 |
86 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)(10,12,14,15)(11,13);(2,3)(4,5)(6,7)(9,12)(10,14)(13,15)Polycyclic presentation:
2^6,7|b^2=c,d^2=f,b^a=bd,c^a=ce,d^a=df,g^a=g^6,d^b=def,e^b=ef,d^c=df46 conjugacy classes — view the full character table.
| maximal subgroup of | #11726884, #11726887, #11726893, … |
| maximal normal subgroup of | #11726884, #11726887, #11726893, … |
| maximal quotient of | #11725254, #11725257, #11725259, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 31);