Finite Group DatabasebetaFinite Group Databasebeta| order | 15894 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #22547287⋊C2 |
| Fitting, socle, derived, Sylow | C883 ⋊ C2×C9 |
| Hall | #22547287 ⋊ C2 |
| Hall | D883 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C883 | C2×C9 |
| prime radical | D883⋊C3 | C3 |
| cosocle | C883⋊C3 | C2×C3 |
| LCS | G ▷ C883 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 883 |
Polycyclic presentation:
2,3^2,883|b^3=c,d^a=d^882,d^b=d^641,d^c=d^54567 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#22547287⋊C2 |
| maximal normal subgroup of | C2×#22547287⋊C2 |
| maximal quotient of | #22547287⋊C4, C2×#22547287⋊C2 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15894, 8);