Finite Group DatabasebetaFinite Group Databasebeta| order | 6720 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| direct product | GL(2,𝔽3)×C7⋊AGL(1,𝔽5) |
| Fitting | C5×C7×Q8 ⋊ C4×D3 |
| derived | C5×C7×SL(2,𝔽3) ⋊ C2×C4 |
| Hall | C5×C7 ⋊ C4×GL(2,𝔽3) |
| Sylow | C7 ⋊ AGL(1,𝔽5)×GL(2,𝔽3) |
| Sylow | C5 ⋊ Dic7×GL(2,𝔽3) |
352 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 352 conjugacy classes of subgroups — too many to draw. Only its 41 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
136 conjugacy classes — view the full character table.
| maximal subgroup of | GL(2,𝔽3)×ΓL(1,𝔽8)⋊AGL(1,𝔽5) |
| maximal normal subgroup of | GL(2,𝔽3)×ΓL(1,𝔽8)⋊AGL(1,𝔽5) |
Past the SmallGroups library coverage — no SmallGroups id.