Finite Group DatabasebetaFinite Group Databasebeta| order | 10404 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3×C17 |
| direct product | C2×C3×(C17⋊D17)⋊C3 |
| unambiguous semidirect product | (C2×C17⋊D17)⋊C32 |
| unambiguous semidirect product | (C2×C3×C17⋊D17)⋊C3 |
| Fitting, socle | C2×C3×C172 ⋊ C2×C3 |
| derived, Sylow | C172 ⋊ C22×C32 |
| Hall | C3×C172⋊C3 ⋊ C22 |
| Hall | C2×C17⋊D17 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | (C17⋊D17)⋊C3 |
| commutator, cosocle, hypocenter | C172 | C22×C32 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C172 | C2×C3 |
| LCS | G ▷ C172 | |
| UCS | C1 ◁ C2×C3 | |
120 conjugacy classes of subgroups.
324 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10404, 110);