Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C4×C5×Q8 ⋊ C2 |
| Sylow | C5 ⋊ #464 |
112 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 112 conjugacy classes of subgroups — too many to draw. Only its 43 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)(10,12,14,20)(11,16,15,24)(13,22,23,19)(17,25,21,18);(6,7,8,9)(11,15)(16,24)(17,21)(18,25);(2,3)(4,5)(7,9)(10,11)(12,18)(13,21)(14,15)(16,19)(17,23)(20,25)(22,24)Polycyclic presentation:
2^6,5|b^2=ef,c^2=f,d^2=f,b^a=be,c^a=cd,d^a=df,g^a=g^4,d^c=df59 conjugacy classes — view the full character table.
| maximal subgroup of | #10611355, #10611358, #10611370, … |
| maximal normal subgroup of | #10611355, #10611358, #10611370, … |
| maximal quotient of | #10600255, #10600257, #10600261, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 655);