Finite Group DatabasebetaFinite Group Databasebeta| order | 6578 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C11 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C13⋊AGL(1,𝔽23) |
| unambiguous semidirect product | (C23⋊C11)⋊D13 |
| unambiguous semidirect product | D299⋊C11 |
| Fitting, socle, derived, Hall | C13×C23 ⋊ C2×C11 |
| Hall | C13×C23⋊C11 ⋊ C2 |
| Hall | D299 ⋊ C11 |
| Hall | C23⋊C11 ⋊ D13 |
| Sylow | C23 ⋊ C11×D13 |
| Sylow | C13 ⋊ AGL(1,𝔽23) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C13×C23 | C2×C11 |
| LCS | G ▷ C13×C23 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
2,11,13,23|c^a=c^12,d^a=d^22,d^b=d^2101 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6578, 12);