Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C7 ⋊ #352 |
68 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)(11,19,20,17)(12,18)(14,22,23,16)(15,21);(2,3)(4,5)(6,7)(8,9,12,15)(10,16,18,22)(11,14,20,23)(13,19,21,17)Polycyclic presentation:
2^6,7|a^2=f,b^2=c,b^a=bd,c^a=ce,g^a=g^6,d^b=de,e^b=ef,d^c=df46 conjugacy classes — view the full character table.
| maximal subgroup of | #11726889, #11726890, D7×#352, … |
| maximal normal subgroup of | #11726889, #11726890, D7×#352, … |
| maximal quotient of | #11725251, #11725253, #11725264, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 29);