Finite Group DatabasebetaFinite Group Databasebeta| order | 3072 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C26 |
| direct product | C2×#72240889 |
| Fitting | C2×#58990 ⋊ D3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | #11715753 |
| commutator, cosocle, hypocenter | #2679⋊C3 | C23 |
| Frattini | C23 | C22×#1020 |
| Fitting | C2×#58990 | D3 |
| socle | C24 | C2×#1020 |
| LCS | G ▷ #2679⋊C3 | |
| UCS | C1 ◁ C22 | |
8890 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 8890 conjugacy classes of subgroups — too many to draw. Only its 49 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 24 |
74 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72240895, C2×#72240902, C2×#72240899 |
| maximal normal subgroup of | C2×#72240895, C2×#72240902, C2×#72240899 |
Past the SmallGroups library coverage — no SmallGroups id.