Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C5 ⋊ #354 |
70 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)(6,8,10,15)(7,11,13,20)(9,18,19,16)(12,21,17,14);(2,3)(4,5)(6,7)(8,14,15,21)(9,17,19,12)(10,13)(11,16)(18,20)Polycyclic presentation:
2^6,5|a^2=c,b^2=f,d^2=f,b^a=bd,d^a=def,e^a=ef,g^a=g^4,c^b=ce,d^b=df,d^c=df41 conjugacy classes — view the full character table.
| maximal subgroup of | #10597951, #10598038, #10598039, … |
| maximal normal subgroup of | #10597951, #10598038, #10598039, … |
| maximal quotient of | #10598123, #10598132, #10598134, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 99);