Finite Group DatabasebetaFinite Group Databasebeta| order | 11421 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(3,𝔽3) |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C27×C47 · Schur multiplier (H2) = C1 |
| direct product | C47×C81⋊C3 |
| unambiguous semidirect product | C81⋊(C3×C47) |
| unambiguous semidirect product | (C47×C81)⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center | C27×C47 | C32 |
| commutator | C3 | C3×C27×C47 |
| Frattini, cosocle | C27 | C32×C47 |
| socle | C3×C47 | C3×C27 |
| prime radical | C32×C47 | C27 |
| LCS | G ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C27×C47 ◁ G | |
32 conjugacy classes of subgroups.
4653 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C47×#10624500, C47×#10624502, C47×#10624503, … |
| maximal normal subgroup of | C47×#10624500, C47×#10624502, C47×#10624503, … |
| maximal quotient of | C47×#10624499, C47×C32⋊C81, C47×C9⋊C81, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11421, 24);