Finite Group DatabasebetaFinite Group Databasebeta| order | 10092 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | C2×#19097943 |
| Fitting, socle | C2×C292 ⋊ D3 |
| derived, Hall | C292⋊C3 ⋊ C22 |
| Sylow | C292 ⋊ C2×D3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #19097943 |
| commutator, cosocle, hypocenter | C292⋊C3 | C22 |
| Frattini | C1 | G |
| Fitting, socle | C2×C292 | D3 |
| LCS | G ▷ C292⋊C3 | |
| UCS | C1 ◁ C2 | |
38 conjugacy classes of subgroups.
370 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#19097943, C2×C3×#19097943, C2×C3⋊#19097943 |
| maximal normal subgroup of | C2×C3×#19097943 |
| maximal quotient of | C2×#29502829, D3×#19097943, C2×C3×#19097943, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10092, 26);