Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| isoclinism | isoclinic class of C5⋊#226 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| direct product | C4×C5⋊GL(2,𝔽3) |
| Fitting | C4×C5×Q8 ⋊ D3 |
| derived | C5×SL(2,𝔽3) ⋊ C2×C4 |
| Sylow | C5 ⋊ C4×GL(2,𝔽3) |
176 conjugacy classes of subgroups; only the 33 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 33 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
88 conjugacy classes — view the full character table.
| maximal subgroup of | #14511676, #14511677, #14511693, … |
| maximal normal subgroup of | #14511676, #14511677, #14511693, … |
| maximal quotient of | C8×C5⋊GL(2,𝔽3), #14511932, C4×#91184, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 6306);