Finite Group DatabasebetaFinite Group Databasebeta| order | 3072 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C26 |
| direct product | C2×#72209645 |
| Fitting | C2×#62817 ⋊ D3 |
| derived | #11710730 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, socle, hypercenter | C23 | #87588 |
| commutator, cosocle, hypocenter | #11710730 | C22 |
| Frattini | C22 | C2×#87588 |
| Fitting | C2×#62817 | D3 |
| LCS | G ▷ #11710730 | |
| UCS | C1 ◁ C23 | |
15937 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 15937 conjugacy classes of subgroups — too many to draw. Only its 60 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 32 |
78 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72216913, C2×#72216969 |
| maximal normal subgroup of | C2×#72216913, C2×#72216969 |
| maximal quotient of | C2×#72340869 |
Past the SmallGroups library coverage — no SmallGroups id.