Finite Group DatabasebetaFinite Group Databasebeta| order | 8112 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C4 |
| direct product | #261×C3⋊#261 |
| Fitting, socle, derived, Hall | C3×C132 ⋊ C42 |
| Sylow | C132 ⋊ C4×Dic3 |
| Sylow | C3 ⋊ #2612 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C132 | C42 |
| prime radical, cosocle | C3×D132 | C22 |
| LCS | G ▷ C3×C132 | |
| UCS | C1 | |
138 conjugacy classes of subgroups; only the 36 normal subgroups are shown.
This group has 138 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.
| transitive degree | μt(G) = 156 |
105 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#2612, #72242014 |
| maximal normal subgroup of | D3×#2612, #72242014 |
Past the SmallGroups library coverage — no SmallGroups id.