Finite Group DatabasebetaFinite Group Databasebeta| order | 6048 |
| isoclinism | isoclinic class of GL(3,𝔽2) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C22×C3 |
| direct product | C22×C32×GL(3,𝔽2) |
| subgroup | G/H | |
|---|---|---|
| center, Fitting, hypercenter | C22×C32 | GL(3,𝔽2) |
| commutator, hypocenter | GL(3,𝔽2) | C22×C32 |
| Frattini | C1 | G |
| LCS | G ▷ GL(3,𝔽2) | |
| UCS | C1 ◁ C22×C32 | |
1058 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 1058 conjugacy classes of subgroups — too many to draw. Only its 60 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
216 conjugacy classes — view the full character table.
| maximal subgroup of | C22×C32×C5×GL(3,𝔽2) |
| maximal normal subgroup of | C22×C32×C5×GL(3,𝔽2) |
| maximal quotient of | C22×C32×C5×GL(3,𝔽2) |
Past the SmallGroups library coverage — no SmallGroups id.