Finite Group DatabasebetaFinite Group Databasebeta| order | 8064 |
| isoclinism | isoclinic class of AGL(3,𝔽2) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C22 |
| direct product | C2×C3×AGL(3,𝔽2) |
| Fitting, socle | C24×C3 ⋊ GL(3,𝔽2) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | AGL(3,𝔽2) |
| commutator, hypocenter | AGL(3,𝔽2) | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C24×C3 | GL(3,𝔽2) |
| cosocle | C23 | C2×C3×GL(3,𝔽2) |
| LCS | G ▷ AGL(3,𝔽2) | |
| UCS | C1 ◁ C2×C3 | |
795 conjugacy classes of subgroups; only the 12 normal subgroups are shown.
This group has 795 conjugacy classes of subgroups — too many to draw. Only its 12 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
66 conjugacy classes — view the full character table.
Past the SmallGroups library coverage — no SmallGroups id.