Finite Group DatabasebetaFinite Group Databasebeta| order | 3072 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C29 |
| direct product | C22×#11709314 |
| Fitting, Sylow | C22×#15947 ⋊ C3 |
| derived | C26 ⋊ C24×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | #11709314 |
| commutator, cosocle, hypocenter | C26 | C24×C3 |
| Frattini | C24 | C24×A4 |
| Fitting | C22×#15947 | C3 |
| socle | C26 | C22×A4 |
| LCS | G ▷ C26 | |
| UCS | C1 ◁ C22 | |
117593 conjugacy classes of subgroups; only the 264 normal subgroups are shown.
This group has 117593 conjugacy classes of subgroups — too many to draw. Only its 264 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 24 |
120 conjugacy classes — view the full character table.
| maximal subgroup of | C22×#72209642, #72256361, #72256423 |
| maximal normal subgroup of | C22×#72209642, #72256361, #72256423 |
Past the SmallGroups library coverage — no SmallGroups id.