Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C5×#103 ⋊ C2 |
| Sylow | C5 ⋊ C4×SD16 |
122 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 122 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) = 17 |
| transitive degree | μt(G) = 160 |
A minimal faithful permutation representation — 3 generators on 17 points:
(1,2,4,5,3)(10,11,13,15)(12,17,16,14);(6,8,9,7)(11,14)(12,16)(15,17);(2,3)(4,5)(6,7,9,8)Polycyclic presentation:
2^6,5|a^2=e,b^2=e,c^2=f,d^2=f,g^a=g^4,c^b=cd,d^b=df,d^c=df56 conjugacy classes — view the full character table.
| maximal subgroup of | #10603967, #10603969, #10603971, … |
| maximal normal subgroup of | #10603967, #10603969, #10603971, … |
| maximal quotient of | #10599005, #10599009, #10599010, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 415);