Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| isoclinism | isoclinic class of C5⋊(#41⋊C3) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2 |
| direct product | C4×C5⋊(#41⋊C3) |
| unambiguous semidirect product | (C4×#713)⋊C3 |
| Hall | C4×#713 ⋊ C3 |
| Sylow | C5 ⋊ C4×#41⋊C3 |
180 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 45 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 320 |
112 conjugacy classes — view the full character table.
| maximal subgroup of | #14511638, #14511639, #14511640, … |
| maximal normal subgroup of | #14511638, #14511639, #14511640, … |
| maximal quotient of | C8×C5⋊(#41⋊C3), #10611636⋊C3, C4×Dic5×SL(2,𝔽3), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 6351);