Finite Group DatabasebetaFinite Group Databasebeta| order | 3300 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(C11⋊#1035) |
| unambiguous semidirect product | C11⋊(C3⋊#1035) |
| Fitting, derived, Hall | C3×C11×C25 ⋊ C4 |
| Hall | C11×C25 ⋊ Dic3 |
| Hall | C3×C25 ⋊ Dic11 |
| Hall | C3×C11 ⋊ #1035 |
| Sylow | C25 ⋊ Dic33 |
| Sylow | C11 ⋊ C3⋊#1035 |
| Sylow | C3 ⋊ C11⋊#1035 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C3×C11×C25 | C4 |
| Frattini | C5 | C3⋊(C11⋊AGL(1,𝔽5)) |
| socle | C3×C5×C11 | AGL(1,𝔽5) |
| prime radical, cosocle | C3×C11×D25 | C2 |
| LCS | G ▷ C3×C11×C25 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 825 |
Polycyclic presentation:
2^2,3,5,11,5|a^2=b,d^5=f,c^a=c^2,d^a=d^2f,e^a=e^10,f^a=f^2,d^b=d^4f^4,f^b=f^4234 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3300, 23);