Finite Group DatabasebetaFinite Group Databasebeta| order | 10611 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(3,𝔽3) |
| automorphism | ? |
| homology | Abelianization (H1) = C33×C131 · Schur multiplier (H2) = C32 |
| direct product | C3×3−1+2×C131 |
| unambiguous semidirect product | C9⋊(C32×C131) |
| unambiguous semidirect product | (C9×C131)⋊C32 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C32×C131 | C32 |
| commutator, Frattini, cosocle | C3 | C33×C131 |
| prime radical | C33×C131 | C3 |
| LCS | G ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C32×C131 ◁ G | |
76 conjugacy classes of subgroups.
4323 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C131×#6857, C131×#6858, C131×#6860, … |
| maximal normal subgroup of | C131×#6857, C131×#6858, C131×#6860, … |
| maximal quotient of | C3×C32⋊C9×C131, C3×C9⋊C9×C131, C9×3−1+2×C131, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10611, 13);