Finite Group DatabasebetaFinite Group Databasebeta| order | 2197 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(3,𝔽13) |
| automorphism | ? |
| homology | Abelianization (H1) = C132 · Schur multiplier (H2) = C132 |
| extraspecial | 13+1+2 |
| unitriangular | UT(3,𝔽13) |
| Heisenberg | H(3,𝔽13) |
| unambiguous semidirect product | C132⋊C13 |
| subgroup | G/H | |
|---|---|---|
| center, commutator, Frattini, socle, cosocle | C13 | C132 |
| LCS | G ▷ C13 ▷ C1 | |
| UCS | C1 ◁ C13 ◁ G | |
| LECS | G ▷ C13 ▷ C1 | |
31 conjugacy classes of subgroups.
| minimal degree | μ(G) = 169 |
| transitive degree | μt(G) = 169 |
Polycyclic presentation:
13^3|b^a=bc181 conjugacy classes — view the full character table.
| maximal subgroup of | H(3,𝔽13)⋊C13, #43270035, #43270036, … |
| maximal normal subgroup of | H(3,𝔽13)⋊C13, #43270035, #43270036, … |
| maximal quotient of | C132⋊C169, H(3,𝔽13)⋊C13, #43270034, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2197, 3);