Finite Group DatabasebetaFinite Group Databasebeta| order | 30240 |
| isoclinism | isoclinic class of GL(3,𝔽2) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32×C5 · Schur multiplier (H2) = C22×C3 |
| direct product | C22×C32×C5×GL(3,𝔽2) |
| subgroup | G/H | |
|---|---|---|
| center, Fitting, hypercenter | C22×C32×C5 | GL(3,𝔽2) |
| commutator, hypocenter | GL(3,𝔽2) | C22×C32×C5 |
| Frattini | C1 | G |
| LCS | G ▷ GL(3,𝔽2) | |
| UCS | C1 ◁ C22×C32×C5 | |
2116 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 2116 conjugacy classes of subgroups — too many to draw. Only its 120 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1080 conjugacy classes. The character table is too large to display.
| automorphism group of | C23×C7×C31 |
| outer automorphism group of | C23×C7×C31 |
Past the SmallGroups library coverage — no SmallGroups id.