Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
| direct product | C2×#4044 |
| Fitting | C2×C5×C4⋊C4 ⋊ C2 |
| Sylow | C5 ⋊ C2×#126 |
246 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 246 conjugacy classes of subgroups — too many to draw. Only its 111 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 160 |
A minimal faithful permutation representation — 4 generators on 23 points:
(1,2)(3,4,6,7,5)(8,10,11,14)(9,13,12,15)(17,21)(20,23);(9,12)(10,14)(16,18,19,22)(17,20,21,23);(4,5)(6,7)(8,9)(10,13)(11,12)(14,15)(16,17)(18,20)(19,21)(22,23);(1,2)68 conjugacy classes — view the full character table.
| maximal subgroup of | #10598922, #10604302, #10604303, … |
| maximal normal subgroup of | #10598922, #10604302, #10604303, … |
| maximal quotient of | C2×#64940, C2×#64943, C2×#64958, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 1184);