Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C5×#137 ⋊ C2 |
| Sylow | C5 ⋊ #455 |
152 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 152 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) = 80 |
A minimal faithful permutation representation — 3 generators on 21 points:
(1,2,4,5,3)(6,8,10,16)(7,11,12,20)(9,19,17,15)(13,21,18,14);(6,7)(8,14)(9,18)(10,12)(11,15)(13,17)(16,21)(19,20);(2,3)(4,5)(9,17)(11,20)(13,18)(15,19)Polycyclic presentation:
2^6,5|c^2=f,e^2=f,c^a=cd,e^a=ef,g^a=g^4,c^b=ce,d^b=df,e^b=ef,e^c=ef38 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#455, #10612023, #10612029, … |
| maximal normal subgroup of | D5×#455, #10612023, #10612029, … |
| maximal quotient of | #10601091, #10601098, #10601099, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 829);