Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| isoclinism | isoclinic class of Dic14 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | (C2×D7)⋊C16 |
| Fitting | C2×C7×C16 ⋊ C2 |
| Sylow | C7 ⋊ C22⋊C16 |
66 conjugacy classes of subgroups.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 224 |
A minimal faithful permutation representation — 2 generators on 27 points:
(1,2,4,6,7,5,3)(9,11)(12,13,14,17,15,18,20,23,16,19,21,24,22,25,26,27);(2,3)(4,5)(6,7)(8,9)(10,11)Polycyclic presentation:
2^6,7|b^2=c,c^2=e,e^2=f,b^a=bd,g^a=g^6136 conjugacy classes — view the full character table.
| maximal subgroup of | #11726806, #11726807, C16×D28, … |
| maximal normal subgroup of | #11726806, #11726807, C16×D28, … |
| maximal quotient of | #11725309, #11725312, #11725328, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 64);