Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C7×M32 ⋊ C2 |
| Sylow | C7 ⋊ #361 |
62 conjugacy classes of subgroups.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 112 |
A minimal faithful permutation representation — 2 generators on 23 points:
(1,2,4,6,7,5,3)(8,9,10,17,18,20,23,21,12,14,19,13,11,15,16,22);(2,3)(4,5)(6,7)(9,13)(10,16)(11,18)(14,17)(15,22)(19,23)(20,21)Polycyclic presentation:
2^6,7|b^2=cd,c^2=ef,e^2=f,b^a=bc,c^a=ce,e^a=ef,g^a=g^6,c^b=cf,d^b=df76 conjugacy classes — view the full character table.
| maximal subgroup of | #11726845, #11726870, #11726880, … |
| maximal normal subgroup of | #11726845, #11726870, #11726880, … |
| maximal quotient of | #11725322, #11725333, #11725366, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 73);