Finite Group DatabasebetaFinite Group Databasebeta| order | 5819 |
| automorphism | ? |
| homology | Abelianization (H1) = C11 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Sylow | C232 ⋊ C11 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C232 | C11 |
| LCS | G ▷ C232 | |
| UCS | C1 | |
10 conjugacy classes of subgroups.
Polycyclic presentation:
11,23^2|b^a=b^2,c^a=c^1359 conjugacy classes — view the full character table.
| maximal subgroup of | #26042790, #26042799, #26042800, … |
| maximal normal subgroup of | #26042790, #26042799, #26042800, … |
| maximal quotient of | C2×#19154124, C3×#19154124, C5×#19154124 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5819, 8);