Finite Group DatabasebetaFinite Group Databasebeta| order | 10890 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊(#10624391⋊C5) |
| unambiguous semidirect product | (C3⋊#10624391)⋊C5 |
| Fitting, socle | C3×C112 ⋊ C5×D3 |
| derived, Hall | C3×C112⋊C3 ⋊ C2×C5 |
| Hall | C3×(C112⋊C3)⋊C5 ⋊ C2 |
| Hall | C3⋊#10624391 ⋊ C5 |
| Hall | #10597243 ⋊ C3⋊D3 |
| Sylow | C112 ⋊ C5×C3⋊D3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C3×C112⋊C3 | C2×C5 |
| Fitting, socle | C3×C112 | C5×D3 |
| LCS | G ▷ C3×C112⋊C3 | |
| UCS | C1 | |
68 conjugacy classes of subgroups.
Polycyclic presentation:
2,5,3^2,11^2|c^a=c^2,d^a=d^2,f^a=e^4f^10,e^b=e^4,f^b=f^4,e^c=e^7f^10,f^c=e^2f^345 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10890, 85);