Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C7×#97 ⋊ C2 |
| Sylow | C7 ⋊ #444 |
104 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)(8,11,12,19,13,20,21,10)(9,14,15,22,17,23,16,18);(8,10,12,11,13,19,21,20)(9,14,16,18,17,23,15,22);(2,3)(4,5)(6,7)(8,9)(10,18)(11,14)(12,15)(13,17)(16,21)(19,22)(20,23)Polycyclic presentation:
2^6,7|b^2=e,c^2=d,d^2=f,e^2=f,b^a=be,e^a=ef,g^a=g^6,c^b=cf82 conjugacy classes — view the full character table.
| maximal subgroup of | #11726844, #11726845, #11728671, … |
| maximal normal subgroup of | #11726844, #11726845, #11728671, … |
| maximal quotient of | #11725830, #11725831, #11725832, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 251);