Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C7×#107 ⋊ C2 |
| Sylow | C7 ⋊ #474 |
108 conjugacy classes of subgroups.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 224 |
A minimal faithful permutation representation — 3 generators on 23 points:
(1,2,4,6,7,5,3)(9,13)(12,15)(16,17,21,23,19,22,18,20);(8,10,11,14)(9,12,13,15)(17,20)(18,21)(22,23);(2,3)(4,5)(6,7)(8,9)(10,12)(11,13)(14,15)(17,20)(18,21)(22,23)Polycyclic presentation:
2^6,7|b^2=d,c^2=ef,e^2=f,c^a=cde,e^a=ef,g^a=g^6,c^b=ce,e^b=ef61 conjugacy classes — view the full character table.
| maximal subgroup of | #11736599, #11736604, C2×#89662, … |
| maximal normal subgroup of | #11736599, #11736604, C2×#89662, … |
| maximal quotient of | #11726541, #11726554, #11726561, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 424);