Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C5×C22⋊C8 ⋊ 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)(10,13,14,21,15,22,12,19)(11,17,16,20,18,24,23,25);(6,7)(8,9)(10,12,15,14)(11,16,18,23)(13,19,22,21)(17,20,24,25);(2,3)(4,5)(10,11)(12,16)(13,20)(14,23)(15,18)(17,21)(19,24)(22,25)Polycyclic presentation:
2^6,5|b^2=f,c^2=d,d^2=f,c^a=cd,d^a=df,g^a=g^4,c^b=ce59 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#65022, #10610341, #10610345, … |
| maximal normal subgroup of | C2×#65022, #10610341, #10610345, … |
| maximal quotient of | #10598902, #10598906, #10598925, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 360);