Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C7×C4⋊C8 ⋊ 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)(10,14)(16,17,21,23,19,22,18,20);(8,10,11,14)(9,12,13,15);(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=e,c^2=def,d^2=f,c^a=cd,d^a=df,g^a=g^6,c^b=ce79 conjugacy classes — view the full character table.
| maximal subgroup of | #11725950, #11725961, #11725962, … |
| maximal normal subgroup of | #11725950, #11725961, #11725962, … |
| maximal quotient of | #11726375, #11726386, #11726396, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 380);