Finite Group DatabasebetaFinite Group Databasebeta| order | 11421 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #6875 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C9×C47 · Schur multiplier (H2) = C1 |
| direct product | C47×#6875 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C3×C47 | C9⋊C9 |
| commutator | C9 | C3×C9×C47 |
| Frattini, cosocle | C3×C9 | C32×C47 |
| prime radical | C32×C47 | 3−1+2 |
| LCS | G ▷ C9 ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C3×C47 ◁ C3×C9×C47 ◁ G | |
40 conjugacy classes of subgroups.
1645 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C47×#6875, C47×#10624709, C47×#10624828, … |
| maximal normal subgroup of | C3×C47×#6875, C47×#10624709, C47×#10624828, … |
| maximal quotient of | C47×#10624462, C47×#10624472, C3×C47×#6875 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11421, 22);