Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C23 |
| direct product | C5×#5432 |
346 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 54 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) = 120 |
A minimal faithful permutation representation — 2 generators on 17 points:
(1,2,3,4,5)(11,13)(14,15,17);(6,7,8,9)(10,11)(12,13)(15,16)140 conjugacy classes — view the full character table.
| maximal subgroup of | C5×#73049, C5×#73145, C5×#85292, … |
| maximal normal subgroup of | C5×#73049, C5×#73145, C5×#85292, … |
| maximal quotient of | C5×#73141, C5×A4⋊#95, C5×#73143, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 6298);