Finite Group DatabasebetaFinite Group Databasebeta| order | 10404 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | C2×#19104513 |
| derived, Hall | #14579583 ⋊ C22 |
| Sylow | C172 ⋊ C2×D9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #19104513 |
| commutator, cosocle, hypocenter | #14579583 | C22 |
| Frattini | C3 | C2×#13181892 |
| Fitting, socle | C2×C3×C172 | D3 |
| LCS | G ▷ #14579583 | |
| UCS | C1 ◁ C2 | |
58 conjugacy classes of subgroups.
348 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10404, 50);