Finite Group DatabasebetaFinite Group Databasebeta| order | 10611 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of AΣL(1,𝔽27) |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C131 · Schur multiplier (H2) = C3 |
| direct product | AΣL(1,𝔽27)×C131 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C3×C131 | H(3,𝔽3) |
| commutator, Frattini, cosocle | C32 | C32×C131 |
| LCS | G ▷ C32 ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C3×C131 ◁ C32×C131 ◁ G | |
40 conjugacy classes of subgroups.
2227 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×AΣL(1,𝔽27)×C131, C131×#6908, C131×#6909, … |
| maximal normal subgroup of | C3×AΣL(1,𝔽27)×C131, C131×#6908, C131×#6909, … |
| maximal quotient of | C131×#6856, C131×#6857, C131×#6858, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10611, 7);