Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C7 ⋊ #344 |
90 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)(9,13,15,16)(11,17)(12,18)(14,21,22,23)(19,20);(2,3)(4,5)(6,7)(8,9,11,14,12,15,19,22)(10,16,17,23,18,13,20,21)Polycyclic presentation:
2^6,7|a^2=c,b^2=d,c^2=f,b^a=be,d^a=df,g^a=g^6,e^b=ef82 conjugacy classes — view the full character table.
| maximal subgroup of | #11726450, #11726453, #11726454, … |
| maximal normal subgroup of | #11726450, #11726453, #11726454, … |
| maximal quotient of | #11725421, #11725423, #11725426, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 90);