Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Fitting | C5×C22⋊C8 ⋊ C2 |
| Sylow | C5 ⋊ #482 |
106 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 106 conjugacy classes of subgroups — too many to draw. Only its 39 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) = 160 |
A minimal faithful permutation representation — 3 generators on 21 points:
(1,2,4,5,3)(7,11)(8,13)(14,15,16,18,17,19,20,21);(6,8)(7,10)(9,13)(11,12)(15,19)(18,21);(2,3)(4,5)(6,7)(8,12)(9,11)(10,13)(15,18)(16,20)(19,21)Polycyclic presentation:
2^6,5|c^2=de,d^2=f,b^a=be,c^a=cd,d^a=df,g^a=g^4,c^b=cef59 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#65026, #10610322, #10610344, … |
| maximal normal subgroup of | C2×#65026, #10610322, #10610344, … |
| maximal quotient of | #10599416, #10599417, #10599418, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 364);