Finite Group DatabasebetaFinite Group Databasebeta| order | 2109 |
| isoclinism | isoclinic class of #14523722 |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C19×C37 ⋊ C3 |
| Sylow | C37 ⋊ C19⋊C3 |
| Sylow | C19 ⋊ C37⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C19×C37 | C3 |
| LCS | G ▷ C19×C37 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| minimal degree | μ(G) = 56 |
| transitive degree | μt(G) = 703 |
Polycyclic presentation:
3,19,37|b^a=b^11,c^a=c^10237 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#14523722, #16862422, #16862426, … |
| maximal normal subgroup of | C2×#14523722, #16862422, #16862426, … |
| maximal quotient of | C2×#14523722, C7×#14523722, #28414267, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2109, 4);