Finite Group DatabasebetaFinite Group Databasebeta| order | 3072 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | C2×#72213204 |
| Fitting | C2×#10304 ⋊ D3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | #11711452 |
| commutator, cosocle, hypocenter | #1273⋊C3 | C23 |
| Frattini | C2×C42 | C22×S4 |
| Fitting | C2×#10304 | D3 |
| socle | C24 | #857⋊C2 |
| LCS | G ▷ #1273⋊C3 | |
| UCS | C1 ◁ C22 | |
1821 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 1821 conjugacy classes of subgroups — too many to draw. Only its 39 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
70 conjugacy classes — view the full character table.
| maximal subgroup of | #72218323 |
| maximal normal subgroup of | #72218323 |
| maximal quotient of | C2×#72213209 |
Past the SmallGroups library coverage — no SmallGroups id.