Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| isoclinism | isoclinic class of #700 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C4 |
| unambiguous semidirect product | #170⋊C8 |
| Sylow | C5 ⋊ #322 |
66 conjugacy classes of subgroups.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 320 |
A minimal faithful permutation representation — 2 generators on 21 points:
(1,2,3,5,4)(6,7,8,10,9,11,12,13)(15,18)(19,21);(2,3,4,5)(14,15,16,19,17,18,20,21)Polycyclic presentation:
2^6,5|a^2=c,b^2=d,c^2=f,d^2=e,b^a=bf,g^a=g^2,g^c=g^456 conjugacy classes — view the full character table.
| maximal subgroup of | #10603806, C8×#700, #10603810, … |
| maximal normal subgroup of | #10603806, C8×#700, #10603810, … |
| maximal quotient of | #10598515, #170⋊C16, #10598640, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 218);