Finite Group DatabasebetaFinite Group Databasebeta| order | 5517 |
| automorphism | ? |
| homology | Abelianization (H1) = C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Sylow | C613 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C613 | C9 |
| LCS | G ▷ C613 | |
| UCS | C1 | |
6 conjugacy classes of subgroups.
Polycyclic presentation:
3^2,613|a^3=b,c^a=c^467,c^b=c^6577 conjugacy classes — view the full character table.
| maximal subgroup of | #19149452⋊C2, C2×#19149452, C3×#19149452, … |
| maximal normal subgroup of | #19149452⋊C2, C2×#19149452, C3×#19149452, … |
| maximal quotient of | C2×#19149452, #30658500, C3×#19149452, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5517, 3);