Finite Group DatabasebetaFinite Group Databasebeta| order | 10404 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3 |
| direct product | C3×#11923883⋊C3 |
| unambiguous semidirect product | #11923883⋊C32 |
| unambiguous semidirect product | (C3×#11923883)⋊C3 |
| Fitting, socle | C3×C172 ⋊ C3×C4 |
| derived, Sylow | C172 ⋊ C32×C4 |
| Hall | C3×C172⋊C3 ⋊ C4 |
| Hall | #11923883 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #11923883⋊C3 |
| commutator, hypocenter | C172 | C32×C4 |
| Frattini | C1 | G |
| Fitting, socle | C3×C172 | C3×C4 |
| prime radical | C3×(C17⋊D17)⋊C3 | C2 |
| cosocle | C17⋊D17 | C2×C32 |
| LCS | G ▷ C172 | |
| UCS | C1 ◁ C3 | |
72 conjugacy classes of subgroups.
108 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10404, 99);