Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×C5×M16 ⋊ C2 |
| Sylow | C5 ⋊ #413 |
150 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 150 conjugacy classes of subgroups — too many to draw. Only its 59 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)(6,9,10,17,11,18,8,15)(7,13,12,20,14,16,19,21);(6,8,11,10)(7,12,14,19)(9,15,18,17)(13,20,16,21);(2,3)(4,5)(6,7)(8,12)(9,16)(10,19)(11,14)(13,18)(15,21)(17,20)Polycyclic presentation:
2^6,5|b^2=f,c^2=d,d^2=f,c^a=ce,d^a=df,g^a=g^4,e^c=ef62 conjugacy classes — view the full character table.
| maximal subgroup of | #10599493, #10599504, #10599512, … |
| maximal normal subgroup of | #10599493, #10599504, #10599512, … |
| maximal quotient of | #10600590, #10600592, #10600651, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 759);