Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C5×#104 ⋊ C2 |
| Sylow | C5 ⋊ #455 |
152 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 39 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 80 |
A minimal faithful permutation representation — 3 generators on 21 points:
(1,2,4,5,3)(6,9,10,8,11,16,19,17)(7,12,13,18,15,20,14,21);(6,8)(7,12)(9,19)(10,16)(11,17)(13,18)(14,21)(15,20);(2,3)(4,5)(6,7)(8,12)(9,18)(10,14)(11,15)(13,19)(16,21)(17,20)Polycyclic presentation:
2^6,5|c^2=d,d^2=f,e^2=f,c^a=cd,d^a=df,g^a=g^4,c^b=ce,e^b=ef,e^c=ef44 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#65114, #10610717, #10610724, … |
| maximal normal subgroup of | C2×#65114, #10610717, #10610724, … |
| maximal quotient of | #10598975, #10598976, #10598983, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 452);