Finite Group DatabasebetaFinite Group Databasebeta| order | 10845 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C5 · Schur multiplier (H2) = C3 |
| direct product | C3×C5×C241⋊C3 |
| unambiguous semidirect product | (C5×C241)⋊C32 |
| unambiguous semidirect product | (C3×C5×C241)⋊C3 |
| Fitting, socle | C3×C5×C241 ⋊ C3 |
| derived, Sylow | C241 ⋊ C32×C5 |
| Hall | C5×C241 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C5 | C241⋊C3 |
| commutator, cosocle, hypocenter | C241 | C32×C5 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C241 | C3 |
| LCS | G ▷ C241 | |
| UCS | C1 ◁ C3×C5 | |
24 conjugacy classes of subgroups.
1245 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C5×D241⋊C3, C3×C5⋊(D241⋊C3), C3×D5×C241⋊C3, … |
| maximal normal subgroup of | C3×C5×D241⋊C3, C3×C5⋊(D241⋊C3), C3×D5×C241⋊C3, … |
| maximal quotient of | C2×C3×C5×C241⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10845, 8);