Finite Group DatabasebetaFinite Group Databasebeta| order | 10404 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2×C17 |
| direct product | C2×#19104523 |
| Fitting, socle | C2×C172 ⋊ C2×C9 |
| derived, Sylow | C172 ⋊ C22×C9 |
| Hall | #14579585 ⋊ C22 |
| Hall | C2×C17⋊D17 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #19104523 |
| commutator, hypocenter | C172 | C22×C9 |
| Frattini | C1 | G |
| Fitting, socle | C2×C172 | C2×C9 |
| prime radical | C2×(C17⋊D17)⋊C3 | C3 |
| cosocle | C172⋊C3 | C22×C3 |
| LCS | G ▷ C172 | |
| UCS | C1 ◁ C2 | |
40 conjugacy classes of subgroups.
68 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10404, 96);