Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C5×C4⋊C8 ⋊ C2 |
| Sylow | C5 ⋊ #464 |
112 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 112 conjugacy classes of subgroups — too many to draw. Only its 41 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 25 |
| transitive degree | μt(G) = 160 |
A minimal faithful permutation representation — 3 generators on 25 points:
(1,2,4,5,3)(7,9)(10,12,13,20,14,19,22,25)(11,16,17,18,15,23,21,24);(6,7,8,9)(11,15)(12,19)(17,21)(20,25);(2,3)(4,5)(7,9)(10,11)(12,18)(13,21)(14,15)(16,20)(17,22)(19,24)(23,25)Polycyclic presentation:
2^6,5|b^2=ef,c^2=d,d^2=f,b^a=be,c^a=cd,d^a=df,g^a=g^4,c^b=ce59 conjugacy classes — view the full character table.
| maximal subgroup of | #10610752, #10610760, #10610761, … |
| maximal normal subgroup of | #10610752, #10610760, #10610761, … |
| maximal quotient of | #10599341, #10599342, #10599347, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 472);