Finite Group DatabasebetaFinite Group Databasebeta| order | 11034 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #19149450⋊C2 |
| derived, Sylow | C613 ⋊ C2×C9 |
| Hall | #19149450 ⋊ C2 |
| Hall | D613 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | D613⋊C3 |
| commutator, hypocenter | C613 | C2×C9 |
| Fitting, socle, cosocle | C3×C613 | C2×C3 |
| prime radical | C3×D613 | C3 |
| LCS | G ▷ C613 | |
| UCS | C1 ◁ C3 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,613,3|b^3=d,c^a=c^612,c^b=c^65324 conjugacy classes — view the full character table.
| maximal subgroup of | #36348160, C2×#19149450⋊C2 |
| maximal normal subgroup of | #36348160, C2×#19149450⋊C2 |
| maximal quotient of | #36348154, C2×#19149450⋊C2 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11034, 2);