Finite Group DatabasebetaFinite Group Databasebeta| order | 10092 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C3×#16809850 |
| Fitting, Hall | C3×C841 ⋊ C4 |
| derived, Sylow | C841 ⋊ C3×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #16809850 |
| commutator, hypocenter | C841 | C3×C4 |
| Frattini | C29 | C3×#1181 |
| Fitting | C3×C841 | C4 |
| socle | C3×C29 | #1181 |
| prime radical | C3×D841 | C2 |
| cosocle | D841 | C2×C3 |
| LCS | G ▷ C841 | |
| UCS | C1 ◁ C3 | |
18 conjugacy classes of subgroups.
642 conjugacy classes — view the full character table.
| maximal subgroup of | C9×#16809850, C32×#16809850, C3×C3⋊#16809850 |
| maximal normal subgroup of | C9×#16809850, C32×#16809850 |
| maximal quotient of | C9×#16809850, C32×#16809850, C3×C3⋊#16809850 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10092, 6);