Finite Group DatabasebetaFinite Group Databasebeta| order | 2880 |
| isoclinism | isoclinic class of #11757163 |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C22 |
| direct product | C3×#11757163 |
| Fitting, socle | C24×C3 ⋊ A5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #11757163 |
| commutator, hypocenter | #11757163 | C3 |
| Frattini | C1 | G |
| Fitting, socle | C24×C3 | A5 |
| cosocle | C24 | C3×A5 |
| LCS | G ▷ #11757163 | |
| UCS | C1 ◁ C3 | |
146 conjugacy classes of subgroups; only the 6 normal subgroups are shown.
This group has 146 conjugacy classes of subgroups — too many to draw. Only its 6 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.
Past the SmallGroups library coverage — no SmallGroups id.