Finite Group DatabasebetaFinite Group Databasebeta| order | 1404 |
| isoclinism | isoclinic class of C27⋊#261 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C27⋊#261 |
| Fitting, derived, Hall | C13×C27 ⋊ C4 |
| Sylow | C27 ⋊ #261 |
| Sylow | C13 ⋊ Dic27 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C13×C27 | C4 |
| Frattini | C9 | C3⋊#261 |
| socle | C3×C13 | Dic9 |
| prime radical | C3×D13 | D9 |
| cosocle | D13×C27 | C2 |
| LCS | G ▷ C13×C27 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| minimal degree | μ(G) = 40 |
| transitive degree | μt(G) = 351 |
Polycyclic presentation:
2^2,3,13,3^2|a^2=b,c^3=e^2,e^3=f^2,c^a=c^2ef,d^a=d^8,e^a=e^2f,f^a=f^2,d^b=d^12111 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1404, 10);