Finite Group DatabasebetaFinite Group Databasebeta| order | 1331 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(3,𝔽11) |
| automorphism | ? |
| homology | Abelianization (H1) = C112 · Schur multiplier (H2) = C112 |
| extraspecial | 11+1+2 |
| unitriangular | UT(3,𝔽11) |
| Heisenberg | H(3,𝔽11) |
| unambiguous semidirect product | C112⋊C11 |
| subgroup | G/H | |
|---|---|---|
| center, commutator, Frattini, socle, cosocle | C11 | C112 |
| LCS | G ▷ C11 ▷ C1 | |
| UCS | C1 ◁ C11 ◁ G | |
| LECS | G ▷ C11 ▷ C1 | |
27 conjugacy classes of subgroups.
| minimal degree | μ(G) = 121 |
| transitive degree | μt(G) = 121 |
Polycyclic presentation:
11^3|b^a=bc131 conjugacy classes — view the full character table.
| maximal subgroup of | H(3,𝔽11)⋊C11, #28410731, #28410732, … |
| maximal normal subgroup of | H(3,𝔽11)⋊C11, #28410731, #28410732, … |
| maximal quotient of | C112⋊C121, H(3,𝔽11)⋊C11, #28410730, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1331, 3);