Finite Group DatabasebetaFinite Group Databasebeta| order | 3888 |
| automorphism | Aut(G) = C22×#10620184⋊C2 (order 5184) · Inn(G) = #10620184 · Out(G) = C23 |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| general linear | GL(2,ℤ/9) |
| direct product | C3×#13049364 |
| derived | SL(2,ℤ/9) ⋊ C2×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | #10620184 |
| commutator, cosocle, hypocenter | SL(2,ℤ/9) | C2×C3 |
| Frattini | C2 | C3×#10620184 |
| Fitting, socle | C2×C34 | S4 |
| LCS | G ▷ SL(2,ℤ/9) | |
| UCS | C1 ◁ C2×C3 | |
324 conjugacy classes of subgroups; only the 14 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 14 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
78 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#72277606 |
| maximal quotient of | C3×#72277606 |
| automorphism group of | C92, C2×C92 |
| outer automorphism group of | C92, C2×C92, #6855 |
Past the SmallGroups library coverage — no SmallGroups id.