Finite Group DatabasebetaFinite Group Databasebeta| order | 2904 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C3×#11757246 |
| Hall | C3×C112 ⋊ D4 |
| Sylow | C112 ⋊ C3×D4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | D112 |
| commutator, cosocle | C2×C112 | C22×C3 |
| Frattini | C2 | C3×D112 |
| Fitting, socle | C2×C3×C112 | C22 |
| hypocenter | C112 | C3×D4 |
| LCS | G ▷ C2×C112 ▷ C112 | |
| UCS | C1 ◁ C2×C3 | |
114 conjugacy classes of subgroups.
| transitive degree | μt(G) = 132 |
285 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×#14515540, D3×#11757246, #72247215, … |
| maximal normal subgroup of | C3×#14515540, D3×#11757246, #72247215, … |
Past the SmallGroups library coverage — no SmallGroups id.