Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C5 ⋊ #388 |
190 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 190 conjugacy classes of subgroups — too many to draw. Only its 69 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)(11,13)(15,17);(6,8,9,7)(14,15)(16,17);(2,3)(4,5)(6,7,9,8)(10,11,12,13)Polycyclic presentation:
2^6,5|a^2=f,b^2=d,c^a=cdf,g^a=g^4,c^b=ce68 conjugacy classes — view the full character table.
| maximal subgroup of | #10605171, C4×#4025, #10605179, … |
| maximal normal subgroup of | #10605171, C4×#4025, #10605179, … |
| maximal quotient of | #10600196, #10600198, #10600207, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 572);