Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C7×#101 ⋊ C2 |
| Sylow | C7 ⋊ #456 |
142 conjugacy classes of subgroups.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 112 |
A minimal faithful permutation representation — 3 generators on 23 points:
(1,2,4,6,7,5,3)(8,11,12,21,13,22,23,14)(9,15,16,20,17,10,18,19);(8,10,13,15)(9,14,17,21)(11,16,22,18)(12,20,23,19);(2,3)(4,5)(6,7)(8,9)(10,14)(11,20)(12,18)(13,17)(15,21)(16,23)(19,22)Polycyclic presentation:
2^6,7|b^2=f,c^2=d,d^2=f,c^a=cd,d^a=df,e^a=ef,g^a=g^6,c^b=ce,d^b=df,e^c=ef49 conjugacy classes — view the full character table.
| maximal subgroup of | #11726915, #11726916, #11726921, … |
| maximal normal subgroup of | #11726915, #11726916, #11726921, … |
| maximal quotient of | #11725886, #11725887, #11725888, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 286);