Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×C5×SD16 ⋊ C2 |
| Sylow | C5 ⋊ #471 |
104 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 104 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) = 80 |
A minimal faithful permutation representation — 3 generators on 21 points:
(1,2,4,5,3)(7,12)(8,15)(9,17)(11,18)(13,14)(16,21);(6,8,9,15,10,16,17,21)(7,11,12,20,14,18,13,19);(2,3)(4,5)(6,7)(8,11)(9,12)(10,14)(13,17)(15,20)(16,18)(19,21)Polycyclic presentation:
2^6,5|b^2=e,d^2=f,e^2=f,c^a=cd,d^a=df,g^a=g^4,c^b=cef,d^c=df,e^c=ef44 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#471, #10612660, #10612661, … |
| maximal normal subgroup of | D5×#471, #10612660, #10612661, … |
| maximal quotient of | #10600988, #10600989, #10600990, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 804);