Finite Group DatabasebetaFinite Group Databasebeta| order | 10845 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C241⋊C5)⋊C9 |
| unambiguous semidirect product | (C241⋊C9)⋊C5 |
| derived, Sylow | C241 ⋊ C5×C9 |
| Hall | C241⋊C9 ⋊ C5 |
| Hall | C241⋊C5 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | (C241⋊C3)⋊C5 |
| commutator, hypocenter | C241 | C5×C9 |
| Fitting, socle, cosocle | C3×C241 | C3×C5 |
| prime radical | C3×C241⋊C5 | C3 |
| LCS | G ▷ C241 | |
| UCS | C1 ◁ C3 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
3,5,241,3|a^3=d,c^a=c^15,c^b=c^9193 conjugacy classes — view the full character table.
| maximal subgroup of | C2×(C241⋊C5)⋊C9, (D241⋊C5)⋊C9 |
| maximal normal subgroup of | C2×(C241⋊C5)⋊C9, (D241⋊C5)⋊C9 |
| maximal quotient of | C2×(C241⋊C5)⋊C9 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10845, 2);