Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4 |
| direct product | C2×#4038 |
| Fitting | C2×C5×C4⋊C4 ⋊ C2 |
| Sylow | C5 ⋊ C2×#117 |
330 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 167 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 160 |
A minimal faithful permutation representation — 4 generators on 19 points:
(3,4,5,6)(7,8,10,11,9)(13,17)(14,18);(1,2)(12,14,15,18)(13,16,17,19);(8,9)(10,11)(12,13)(14,16)(15,17)(18,19);(1,2)80 conjugacy classes — view the full character table.
| maximal subgroup of | #10598917, #10598919, #10599606, … |
| maximal normal subgroup of | #10598917, #10598919, #10599606, … |
| maximal quotient of | C2×#64937, C2×#64955, C2×#64940, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 1174);