Finite Group DatabasebetaFinite Group Databasebeta| order | 2016 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C2 |
| direct product | Dic3×GL(3,𝔽2) |
| derived | C3×GL(3,𝔽2) ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D3×GL(3,𝔽2) |
| commutator, hypocenter | C3×GL(3,𝔽2) | C4 |
| Fitting, cosocle | C2×C3 | C2×GL(3,𝔽2) |
| socle, prime radical | C2×C3×GL(3,𝔽2) | C2 |
| LCS | G ▷ C3×GL(3,𝔽2) | |
| UCS | C1 ◁ C2 | |
143 conjugacy classes of subgroups; only the 10 normal subgroups are shown.
This group has 143 conjugacy classes of subgroups — too many to draw. Only its 10 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
36 conjugacy classes — view the full character table.
| maximal subgroup of | SL(2,𝔽5)×GL(3,𝔽2), #226×GL(3,𝔽2), Dic3×AGL(3,𝔽2), … |
| maximal normal subgroup of | C4×D3×GL(3,𝔽2) |
| maximal quotient of | Dic3×SL(2,𝔽7), Dic3×AGL(3,𝔽2) |
Past the SmallGroups library coverage — no SmallGroups id.