Finite Group DatabasebetaFinite Group Databasebeta| order | 26604 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #20268985⋊C4 |
| derived, Sylow | C739 ⋊ C4×C9 |
| Hall | #20268985 ⋊ C4 |
| Hall | Dic739 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2×C3 | D739⋊C3 |
| commutator, hypocenter | C739 | C4×C9 |
| Fitting, socle, prime radical, cosocle | C2×C3×C739 | C2×C3 |
| LCS | G ▷ C739 | |
| UCS | C1 ◁ C2×C3 | |
18 conjugacy classes of subgroups.
| transitive degree | μt(G) = 26604 |
Polycyclic presentation:
2,3,739,2,3|a^2=d,b^3=e,c^a=c^738,c^b=c^320774 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26604, 2);