Finite Group DatabasebetaFinite Group Databasebeta| order | 11005 |
| isoclinism | isoclinic class of ΓL(1,𝔽32) |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C71 · Schur multiplier (H2) = C1 |
| direct product | C71×ΓL(1,𝔽32) |
| unambiguous semidirect product | C31⋊(C5×C71) |
| Fitting, socle, Hall | C31×C71 ⋊ C5 |
| derived, Sylow | C31 ⋊ C5×C71 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C71 | ΓL(1,𝔽32) |
| commutator, cosocle, hypocenter | C31 | C5×C71 |
| Frattini | C1 | G |
| Fitting, socle | C31×C71 | C5 |
| LCS | G ▷ C31 | |
| UCS | C1 ◁ C71 | |
8 conjugacy classes of subgroups.
781 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C71×ΓL(1,𝔽32), D71×ΓL(1,𝔽32), C71×D31⋊C5, … |
| maximal normal subgroup of | C2×C71×ΓL(1,𝔽32), D71×ΓL(1,𝔽32), C71×D31⋊C5, … |
| maximal quotient of | C2×C71×ΓL(1,𝔽32), C3×C71×ΓL(1,𝔽32) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11005, 1);