Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C5×#104 ⋊ C2 |
| Sylow | C5 ⋊ #443 |
106 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 106 conjugacy classes of subgroups — too many to draw. Only its 45 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)(6,9,10,17,12,18,11,8)(7,13,14,20,15,21,19,16);(6,8)(7,13)(9,10)(11,18)(12,17)(14,20)(15,21)(16,19);(2,3)(4,5)(6,7)(8,16)(9,13)(10,14)(11,19)(12,15)(17,20)(18,21)Polycyclic presentation:
2^6,5|c^2=d,d^2=f,e^2=f,b^a=be,e^a=ef,g^a=g^4,c^b=cef,e^b=ef,e^c=ef56 conjugacy classes — view the full character table.
| maximal subgroup of | #10603999, #10604000, C2×#65113, … |
| maximal normal subgroup of | #10603999, #10604000, C2×#65113, … |
| maximal quotient of | #10598941, #10598942, #10598949, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 451);