Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C7 ⋊ #354 |
70 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)(8,10,12,17)(9,13,15,22)(11,20,21,18)(14,23,19,16);(2,3)(4,5)(6,7)(8,9)(10,16,17,23)(11,19,21,14)(12,15)(13,18)(20,22)Polycyclic presentation:
2^6,7|a^2=c,b^2=f,d^2=f,b^a=bd,d^a=def,e^a=ef,g^a=g^6,c^b=ce,d^b=df,d^c=df55 conjugacy classes — view the full character table.
| maximal subgroup of | #11725266, #11725353, #11725354, … |
| maximal normal subgroup of | #11725266, #11725353, #11725354, … |
| maximal quotient of | #11725438, #11725447, #11725449, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 98);