Finite Group DatabasebetaFinite Group Databasebeta| order | 15893 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C691⋊C23 |
| Fitting, socle, derived, Sylow | C691 ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C691 | C23 |
| LCS | G ▷ C691 | |
| UCS | C1 | |
4 conjugacy classes of subgroups.
Polycyclic presentation:
23,691|b^a=b^27153 conjugacy classes — view the full character table.
| maximal subgroup of | D691⋊C23, C2×C691⋊C23 |
| maximal normal subgroup of | D691⋊C23, C2×C691⋊C23 |
| maximal quotient of | C2×C691⋊C23 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15893, 1);