Finite Group DatabasebetaFinite Group Databasebeta| order | 7920 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C3×#72223869 |
| derived | SL(2,𝔽11) ⋊ C2×C3 |
| subgroup | G/H | |
|---|---|---|
| center, Fitting, hypercenter | C3×C4 | PSL(2,𝔽11) |
| commutator, hypocenter | SL(2,𝔽11) | C2×C3 |
| Frattini, cosocle | C2 | C2×C3×PSL(2,𝔽11) |
| socle | C2×C3 | C2×PSL(2,𝔽11) |
| LCS | G ▷ SL(2,𝔽11) | |
| UCS | C1 ◁ C3×C4 | |
116 conjugacy classes of subgroups.
90 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#72223873 |
| maximal normal subgroup of | C3×#72223873 |
Past the SmallGroups library coverage — no SmallGroups id.