Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| isoclinism | isoclinic class of Dic14 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | Dic7⋊C16 |
| Sylow | C7 ⋊ C4⋊C16 |
50 conjugacy classes of subgroups.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 448 |
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|a^2=d,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 | C16×Dic14, #11726802, #11726806, … |
| maximal normal subgroup of | C16×Dic14, #11726802, #11726806, … |
| maximal quotient of | #11725360, #11725361, Dic7⋊C32, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 58);