Finite Group DatabasebetaFinite Group Databasebeta| order | 10860 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C3×#16813738 |
| Fitting, socle, Hall | C3×C5×C181 ⋊ C4 |
| derived, Hall | C5×C181 ⋊ C3×C4 |
| Hall | C3×C181 ⋊ AGL(1,𝔽5) |
| Sylow | C181 ⋊ C3×AGL(1,𝔽5) |
| Hall | C3×C5 ⋊ #10624382 |
| Sylow | C5 ⋊ C3×#10624382 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #16813738 |
| commutator, hypocenter | C5×C181 | C3×C4 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C181 | C4 |
| prime radical | C3×D905 | C2 |
| cosocle | D905 | C2×C3 |
| LCS | G ▷ C5×C181 | |
| UCS | C1 ◁ C3 | |
24 conjugacy classes of subgroups.
690 conjugacy classes — view the full character table.
| maximal subgroup of | #45656359, C9×#16813738, C3×#16813738⋊C3, … |
| maximal normal subgroup of | #45656359, C9×#16813738, C3×#16813738⋊C3, … |
| maximal quotient of | C9×#16813738, C32×#16813738, C3×C3⋊#16813738 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10860, 45);