Finite Group DatabasebetaFinite Group Databasebeta| order | 10860 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×Dic181⋊C3 |
| unambiguous semidirect product | (C5×Dic181)⋊C3 |
| derived, Sylow | C181 ⋊ C3×C4×C5 |
| Hall | C5×Dic181 ⋊ C3 |
| Hall | C5×C181⋊C3 ⋊ C4 |
| Hall | C5×C181 ⋊ C3×C4 |
| Hall | Dic181 ⋊ C3×C5 |
| Hall | C181⋊C3 ⋊ C4×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | D181⋊C3 |
| commutator, hypocenter | C181 | C3×C4×C5 |
| Frattini | C2 | C5×D181⋊C3 |
| Fitting, socle | C2×C5×C181 | C2×C3 |
| prime radical | C2×C5×C181⋊C3 | C2 |
| cosocle | C2×C181 | C2×C3×C5 |
| LCS | G ▷ C181 | |
| UCS | C1 ◁ C2×C5 | |
24 conjugacy classes of subgroups.
360 conjugacy classes — view the full character table.
| maximal subgroup of | C5×#20266783, C3×C5×Dic181⋊C3, C5×C3⋊(Dic181⋊C3) |
| maximal normal subgroup of | C5×#20266783, C3×C5×Dic181⋊C3 |
| maximal quotient of | C5×#20266765, C3×C5×Dic181⋊C3, C5×C3⋊(Dic181⋊C3) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10860, 15);