Finite Group DatabasebetaFinite Group Databasebeta| order | 2304 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22×C3 |
| direct product | C2×#11923442 |
| derived | A42 ⋊ C2×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | #10596770 |
| commutator, hypocenter | A42 | C2×C8 |
| Frattini | C2 | C2×#10596770 |
| Fitting, socle | C26 | #157 |
| prime radical | C22×A42 | C4 |
| cosocle | A4⋊SL(2,ℤ/4) | C22 |
| LCS | G ▷ A42 | |
| UCS | C1 ◁ C22 | |
498 conjugacy classes of subgroups; only the 21 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 21 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
52 conjugacy classes — view the full character table.
| maximal subgroup of | #72209937 |
| maximal quotient of | #72227892 |
Past the SmallGroups library coverage — no SmallGroups id.