Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C5×C22⋊C8 ⋊ C2 |
| Sylow | C5 ⋊ #435 |
124 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 124 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)(7,9)(10,11,12,15,13,14,16,17);(6,7)(8,9)(11,14)(15,17);(2,3)(4,5)(7,9)Polycyclic presentation:
2^6,5|c^2=d,d^2=f,b^a=bef,g^a=g^4,c^b=ce68 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#65017, #10610327, #10610334, … |
| maximal normal subgroup of | C2×#65017, #10610327, #10610334, … |
| maximal quotient of | #10598946, #10598948, #10598951, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 355);