Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Fitting | C5×#102 ⋊ C2 |
| Sylow | C5 ⋊ #490 |
110 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 110 conjugacy classes of subgroups — too many to draw. Only its 37 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)(6,8,9,13)(7,11,10,12)(14,15)(16,21)(17,18)(19,20);(7,10)(11,12)(15,19)(16,20)(18,21);(2,3)(4,5)(6,7,9,10)(8,12,13,11)(15,18)(19,21)Polycyclic presentation:
2^6,5|a^2=e,c^2=e,d^2=f,b^a=be,c^a=cef,g^a=g^4,c^b=cd,d^b=df,d^c=df44 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#65053, #10610468, #10610493, … |
| maximal normal subgroup of | C2×#65053, #10610468, #10610493, … |
| maximal quotient of | #10599598, #10599604, #10599636, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 391);