Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| isoclinism | isoclinic class of #64686 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C5 ⋊ H(3,ℤ/4) |
94 conjugacy classes of subgroups.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 80 |
A minimal faithful permutation representation — 2 generators on 21 points:
(1,2,4,5,3)(6,8,9,17,11,16,10,18)(7,12,13,15,14,20,19,21);(2,3)(4,5)(6,7)(8,15,16,21)(9,19)(10,13)(11,14)(12,18,20,17)Polycyclic presentation:
2^6,5|a^2=c,b^2=d,d^2=f,e^2=f,b^a=be,d^a=df,g^a=g^4,c^b=cf62 conjugacy classes — view the full character table.
| maximal subgroup of | #10598025, #10598027, #10598269, … |
| maximal normal subgroup of | #10598025, #10598027, #10598269, … |
| maximal quotient of | #10598151, #10598157, #10598167, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 115);