Finite Group DatabasebetaFinite Group Databasebeta| order | 26604 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3 |
| direct product | C3×(C739⋊C3)⋊C4 |
| unambiguous semidirect product | (C739⋊C3)⋊(C3×C4) |
| unambiguous semidirect product | Dic739⋊C32 |
| unambiguous semidirect product | (C3×Dic739)⋊C3 |
| derived, Sylow | C739 ⋊ C32×C4 |
| Hall | C3×C739⋊C3 ⋊ C4 |
| Hall | Dic739 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | D739⋊C3 |
| commutator, hypocenter | C739 | C32×C4 |
| Frattini | C2 | C3×D739⋊C3 |
| Fitting, socle | C2×C3×C739 | C2×C3 |
| prime radical | C2×C3×C739⋊C3 | C2 |
| cosocle | C2×C739 | C2×C32 |
| LCS | G ▷ C739 | |
| UCS | C1 ◁ C2×C3 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8868 |
774 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26604, 19);