Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| isoclinism | isoclinic class of #89332 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C7 ⋊ #328 |
80 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)(9,12)(11,15)(13,14)(16,17,19,21)(18,22,23,20);(2,3)(4,5)(6,7)(8,9)(10,14,15,12)(11,13)(17,20,21,22)Polycyclic presentation:
2^6,7|a^2=c,b^2=f,d^2=f,b^a=bd,d^a=def,g^a=g^6,c^b=ce,d^b=df61 conjugacy classes — view the full character table.
| maximal subgroup of | #11726062, #11726063, #11726064, … |
| maximal normal subgroup of | #11726062, #11726063, #11726064, … |
| maximal quotient of | #11725430, #11725444, #11725448, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 95);