Finite Group DatabasebetaFinite Group Databasebeta| order | 1404 |
| isoclinism | isoclinic class of #10622032 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived | C9×C13 ⋊ C3×C4 |
| Hall | #66849 ⋊ C4 |
| Sylow | C13 ⋊ 3−1+2⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #10622032 |
| commutator, hypocenter | C9×C13 | C3×C4 |
| Frattini | C2×C3 | D3×C13⋊C3 |
| Fitting, cosocle | C2×C9×C13 | C2×C3 |
| socle | C2×C3×C13 | C3×D3 |
| prime radical | C2×C3×C13⋊C3 | D3 |
| LCS | G ▷ C9×C13 | |
| UCS | C1 ◁ C2 | |
40 conjugacy classes of subgroups.
| minimal degree | μ(G) = 26 |
| transitive degree | μt(G) = 468 |
Polycyclic presentation:
2,3,2,3,13,3|a^2=c,d^3=f,d^a=d^2f^2,f^a=f^2,d^b=df^2,e^b=e^368 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1404, 26);