Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C5×C22⋊Q8 ⋊ C2 |
| Sylow | C5 ⋊ #452 |
152 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 152 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)(7,9)(10,13,15,21)(11,17,18,25)(12,19,14,23)(16,24,22,20);(6,7)(8,9)(10,12,15,14)(11,16,18,22)(13,19,21,23)(17,24,25,20);(2,3)(4,5)(10,11)(12,16)(13,20)(14,22)(15,18)(17,19)(21,24)(23,25)Polycyclic presentation:
2^6,5|b^2=f,c^2=f,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 | #10611873, #10611874, #10611879, … |
| maximal normal subgroup of | #10611873, #10611874, #10611879, … |
| maximal quotient of | #10600299, #10600315, #10600316, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 674);