Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C5×#99 ⋊ C2 |
| Sylow | C5 ⋊ #410 |
158 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 158 conjugacy classes of subgroups — too many to draw. Only its 51 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 80 |
A minimal faithful permutation representation — 3 generators on 21 points:
(1,2,4,5,3)(6,9)(7,12)(8,14,15,16)(10,17)(11,18,19,20)(13,21);(6,8)(7,11)(9,16)(10,15)(12,20)(13,19)(14,17)(18,21);(2,3)(4,5)(6,7,10,13)(8,11,15,19)(9,12,17,21)(14,18,16,20)Polycyclic presentation:
2^6,5|a^2=f,c^2=d,g^a=g^4,c^b=ce,d^b=df,e^c=ef44 conjugacy classes — view the full character table.
| maximal subgroup of | #10598569, #10598570, #10599929, … |
| maximal normal subgroup of | #10598569, #10598570, #10599929, … |
| maximal quotient of | #10598893, #10598894, #10598895, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 367);