Finite Group DatabasebetaFinite Group Databasebeta| order | 12288 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C2 |
| direct product | C2×#72210257 |
| Fitting, Sylow | C2×#72210251 ⋊ C3 |
| derived | #72210251 ⋊ C2×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | #72210253 |
| commutator, cosocle, hypocenter | #72210251 | C2×C3 |
| Frattini | #94852 | C2×A4 |
| Fitting | C2×#72210251 | C3 |
| socle | C24 | #7014⋊C3 |
| LCS | G ▷ #72210251 | |
| UCS | C1 ◁ C2×C4 | |
1010 conjugacy classes of subgroups; only the 36 normal subgroups are shown.
This group has 1010 conjugacy classes of subgroups — too many to draw. Only its 36 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
192 conjugacy classes — view the full character table.
| maximal subgroup of | SL(2,ℤ/32) |
| maximal normal subgroup of | SL(2,ℤ/32) |
Past the SmallGroups library coverage — no SmallGroups id.