Finite Group DatabasebetaFinite Group Databasebeta| order | 6600 |
| isoclinism | isoclinic class of SL(2,𝔽11) |
| automorphism | ? |
| homology | Abelianization (H1) = C5 · Schur multiplier (H2) = C1 |
| direct product | C5×SL(2,𝔽11) |
| subgroup | G/H | |
|---|---|---|
| center, Fitting, socle, hypercenter | C2×C5 | PSL(2,𝔽11) |
| commutator, hypocenter | SL(2,𝔽11) | C5 |
| Frattini, cosocle | C2 | C5×PSL(2,𝔽11) |
| LCS | G ▷ SL(2,𝔽11) | |
| UCS | C1 ◁ C2×C5 | |
54 conjugacy classes of subgroups.
75 conjugacy classes — view the full character table.
| maximal subgroup of | C5×#72210865 |
| maximal normal subgroup of | C5×#72210865 |
Past the SmallGroups library coverage — no SmallGroups id.