Finite Group DatabasebetaFinite Group Databasebeta| order | 10845 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C5 · Schur multiplier (H2) = C3 |
| direct product | C32×C241⋊C5 |
| unambiguous semidirect product | (C32×C241)⋊C5 |
| Fitting, socle, Hall | C32×C241 ⋊ C5 |
| derived, Sylow | C241 ⋊ C32×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | C241⋊C5 |
| commutator, cosocle, hypocenter | C241 | C32×C5 |
| Frattini | C1 | G |
| Fitting, socle | C32×C241 | C5 |
| LCS | G ▷ C241 | |
| UCS | C1 ◁ C32 | |
24 conjugacy classes of subgroups.
477 conjugacy classes — view the full character table.
| maximal subgroup of | C32×D241⋊C5, C3×C3⋊(D241⋊C5), C3×D3×C241⋊C5, … |
| maximal normal subgroup of | C32×D241⋊C5, C3×C3⋊(D241⋊C5), C3×D3×C241⋊C5, … |
| maximal quotient of | C2×C32×C241⋊C5 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10845, 7);