Finite Group DatabasebetaFinite Group Databasebeta| order | 6144 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C213 |
| direct product | C22×#72209642 |
| Fitting | C22×#15947 ⋊ D3 |
| derived | C22⋊(C22⋊A4) ⋊ C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | #72209642 |
| commutator, cosocle, hypocenter | C22⋊(C22⋊A4) | C25 |
| Frattini | C24 | C24×S4 |
| Fitting | C22×#15947 | D3 |
| socle | C26 | C22×S4 |
| LCS | G ▷ C22⋊(C22⋊A4) | |
| UCS | C1 ◁ C22 | |
332713 conjugacy classes of subgroups; only the 561 normal subgroups are shown.
This group has 332713 conjugacy classes of subgroups — too many to draw. Only its 561 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 24 |
180 conjugacy classes — view the full character table.
| maximal subgroup of | #72256496 |
| maximal normal subgroup of | #72256496 |
Past the SmallGroups library coverage — no SmallGroups id.