Finite Group DatabasebetaFinite Group Databasebeta| order | 3072 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C28 |
| direct product | C2×#72257994 |
| Fitting | C23×#585 ⋊ D3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | #87588 |
| commutator, cosocle, hypocenter | C22⋊#997 | C23 |
| Frattini | C2 | C22×#87588 |
| Fitting | C23×#585 | D3 |
| socle | C24 | C2×#1020 |
| LCS | G ▷ C22⋊#997 | |
| UCS | C1 ◁ C2×C4 | |
At least 9234 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has at least 9234 conjugacy classes of subgroups — too many to draw. Only its 102 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
116 conjugacy classes — view the full character table.
| maximal subgroup of | #72267358 |
| maximal normal subgroup of | #72267358 |
| maximal quotient of | #72267358 |
Past the SmallGroups library coverage — no SmallGroups id.