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 ⋊ #421 |
154 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 154 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)(6,8,9,17,11,16,10,19)(7,12,13,21,14,20,18,15);(8,16)(12,20)(15,21)(17,19);(2,3)(4,5)(6,7)(8,15)(9,13)(10,18)(11,14)(12,17)(16,21)(19,20)Polycyclic presentation:
2^6,5|c^2=d,d^2=f,e^2=f,c^a=ce,e^a=ef,g^a=g^4,c^b=cf,e^c=ef62 conjugacy classes — view the full character table.
| maximal subgroup of | #10599498, #10599501, #10599518, … |
| maximal normal subgroup of | #10599498, #10599501, #10599518, … |
| maximal quotient of | #10600591, #10600592, #10600594, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 766);