Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C5×#104 ⋊ C2 |
| Sylow | C5 ⋊ #421 |
154 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 51 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)(6,9,10,8,11,16,19,17)(7,13,14,20,15,18,21,12);(6,8)(7,12)(9,19)(10,16)(11,17)(13,14)(15,20)(18,21);(2,3)(4,5)(6,7)(8,12)(9,18)(10,14)(11,15)(13,16)(17,20)(19,21)Polycyclic presentation:
2^6,5|c^2=d,d^2=f,e^2=f,c^a=cf,g^a=g^4,c^b=ce,e^b=ef,e^c=ef50 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#65110, #10610714, D5×#421, … |
| maximal normal subgroup of | C2×#65110, #10610714, D5×#421, … |
| maximal quotient of | #10598959, #10598960, #10598961, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 448);