Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| isoclinism | isoclinic class of #1141 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | Q8⋊(C7⋊C8) |
| Sylow | C7 ⋊ Q8⋊C8 |
70 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)(16,17,19,21)(18,23,22,20);(2,3)(4,5)(6,7)(8,9,10,12,11,13,14,15)(17,20)(18,22)(21,23)Polycyclic presentation:
2^6,7|a^2=c,b^2=f,c^2=e,d^2=f,b^a=bd,d^a=df,g^a=g^6,d^b=df88 conjugacy classes — view the full character table.
| maximal subgroup of | D7×Q8⋊C8, #11725983, #11725984, … |
| maximal normal subgroup of | D7×Q8⋊C8, #11725983, #11725984, … |
| maximal quotient of | #11725425, #11725444, #11725448, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 92);