Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| isoclinism | isoclinic class of #89282 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C7 ⋊ #365 |
42 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)(9,13,14,15)(10,17)(11,19)(16,22,20,21)(18,23);(2,3)(4,5)(6,7)(8,9,10,15,11,16,17,22,12,14,18,13,19,20,23,21)Polycyclic presentation:
2^6,7|a^2=d,b^2=c,d^2=e,e^2=f,b^a=bde,c^a=cf,g^a=g^6,d^b=de,e^b=ef58 conjugacy classes — view the full character table.
| maximal subgroup of | #11727000, #11727001, #11727002, … |
| maximal normal subgroup of | #11727000, #11727001, #11727002, … |
| maximal quotient of | #11725270, #11725526, C2×#89282, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 44);