Finite Group DatabasebetaFinite Group Databasebeta| order | 3072 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C25 |
| direct product | C2×#72213856 |
| Fitting, Sylow | C2×#6342420 ⋊ C3 |
| derived | C44 ⋊ C22×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #72213856 |
| commutator, cosocle, hypocenter | C44 | C22×C3 |
| Frattini | C24 | C22×C22⋊A4 |
| Fitting | C2×#6342420 | C3 |
| socle | C25 | C2×C22⋊A4 |
| LCS | G ▷ C44 | |
| UCS | C1 ◁ C2 | |
6060 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 6060 conjugacy classes of subgroups — too many to draw. Only its 92 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
112 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72213872, C2×#72214078 |
| maximal normal subgroup of | C2×#72213872, C2×#72214078 |
Past the SmallGroups library coverage — no SmallGroups id.