Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C7 ⋊ #360 |
58 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)(11,20)(12,14)(13,21)(15,19)(16,22)(18,23);(2,3)(4,5)(6,7)(9,13,14,22)(10,16)(11,19)(15,17,20,23)(18,21)Polycyclic presentation:
2^6,7|a^2=c,d^2=e,e^2=f,b^a=bd,d^a=de,e^a=ef,g^a=g^6,c^b=cf,d^b=def,e^b=ef58 conjugacy classes — view the full character table.
| maximal subgroup of | #11727000, #11727001, D7×#360, … |
| maximal normal subgroup of | #11727000, #11727001, D7×#360, … |
| maximal quotient of | #11725532, #11725568, #11725570, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 123);