Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| isoclinism | isoclinic class of #89246 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C7 ⋊ #330 |
60 conjugacy classes of subgroups.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 2 generators on 23 points:
(1,2,4,6,7,5,3)(9,12,13,14)(16,18,19,17,21,22,20,23);(2,3)(4,5)(6,7)(8,9)(10,12)(11,13)(14,15)(16,17,21,23)(18,19,22,20)Polycyclic presentation:
2^6,7|a^2=f,b^2=c,c^2=f,d^2=ef,b^a=bd,c^a=ce,d^a=def,g^a=g^6,d^b=df79 conjugacy classes — view the full character table.
| maximal subgroup of | #11726095, #11726098, #11726100, … |
| maximal normal subgroup of | #11726095, #11726098, #11726100, … |
| maximal quotient of | #11725283, #11725284, #11725465, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 22);