Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C7×#101 ⋊ C2 |
| Sylow | C7 ⋊ #413 |
150 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)(8,10,11,17,12,18,20,23)(9,14,15,21,13,16,19,22);(8,9,12,13)(10,16,18,14)(11,19,20,15)(17,21,23,22);(2,3)(4,5)(6,7)(9,13)(14,16)(15,19)(21,22)Polycyclic presentation:
2^6,7|b^2=f,c^2=d,d^2=f,b^a=bf,g^a=g^6,c^b=ce,d^b=df,e^c=ef55 conjugacy classes — view the full character table.
| maximal subgroup of | #11726919, #11726920, #11726926, … |
| maximal normal subgroup of | #11726919, #11726920, #11726926, … |
| maximal quotient of | #11725878, #11725880, #11725883, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 285);