Finite Group DatabasebetaFinite Group Databasebeta| order | 11034 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #19149452⋊C2 |
| Fitting, socle, derived, Sylow | C613 ⋊ C2×C9 |
| Hall | #19149452 ⋊ C2 |
| Hall | D613 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C613 | C2×C9 |
| prime radical | D613⋊C3 | C3 |
| cosocle | C613⋊C3 | C2×C3 |
| LCS | G ▷ C613 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2,3^2,613|b^3=c,d^a=d^612,d^b=d^592,d^c=d^54752 conjugacy classes — view the full character table.
| maximal subgroup of | #36348184, C2×#19149452⋊C2 |
| maximal normal subgroup of | #36348184, C2×#19149452⋊C2 |
| maximal quotient of | #36348172, C2×#19149452⋊C2 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11034, 8);