Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| 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)(6,7)(8,9)(11,16)(12,19)(13,21)(15,22)(17,18)(23,24);(6,7,8,9)(10,12)(11,15)(13,20)(14,19)(16,24)(17,22)(18,23)(21,25);(2,3)(4,5)(6,7,8,9)(10,11,14,18)(12,15,19,23)(13,16,21,17)(20,24,25,22)Polycyclic presentation:
2^6,5|a^2=e,b^2=ef,d^2=f,c^a=cd,d^a=df,g^a=g^4,c^b=ce,d^c=df47 conjugacy classes — view the full character table.
| maximal subgroup of | #10612235, #10612237, #10612241, … |
| maximal normal subgroup of | #10612235, #10612237, #10612241, … |
| maximal quotient of | #10600333, #10600334, #10600352, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 681);