Finite Group DatabasebetaFinite Group Databasebeta| order | 11421 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 28973376 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C32×C9 |
| abelian | C3×C92×C47 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C32 | C33×C47 |
| socle, prime radical | C33×C47 | C32 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
252 conjugacy classes of subgroups.
11421 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C47×#10624445, C47×#10624446, C47×#10624463, … |
| maximal normal subgroup of | C47×#10624445, C47×#10624446, C47×#10624463, … |
| maximal quotient of | C93×C47, C3×C47×#6855, C47×#10624544, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11421, 31);