Finite Group DatabasebetaFinite Group Databasebeta| order | 10092 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C29 |
| direct product | C3×#16809858 |
| Fitting, socle, Hall | C3×C292 ⋊ C4 |
| derived, Sylow | C292 ⋊ C3×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #16809858 |
| commutator, hypocenter | C292 | C3×C4 |
| Frattini | C1 | G |
| Fitting, socle | C3×C292 | C4 |
| prime radical | C3×C29⋊D29 | C2 |
| cosocle | C29⋊D29 | C2×C3 |
| LCS | G ▷ C292 | |
| UCS | C1 ◁ C3 | |
80 conjugacy classes of subgroups.
642 conjugacy classes — view the full character table.
| maximal subgroup of | C9×#16809858, C3×#23758666, C32×#16809858, … |
| maximal normal subgroup of | C9×#16809858, C32×#16809858 |
| maximal quotient of | C9×#16809858, C32×#16809858, C3×C3⋊#16809858 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10092, 30);