Finite Group DatabasebetaFinite Group Databasebeta| order | 3300 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C11⋊C5×ΓL(1,𝔽16) |
| unambiguous semidirect product | C3⋊(AGL(1,𝔽5)×C11⋊C5) |
| unambiguous semidirect product | (C11×ΓL(1,𝔽16))⋊C5 |
| Fitting, socle, derived | C3×C5×C11 ⋊ C4×C5 |
| Hall | C3×C5×C11⋊C5 ⋊ C4 |
| Hall | C5×C11⋊C5 ⋊ Dic3 |
| Hall | C3×C11 ⋊ C5×AGL(1,𝔽5) |
| Sylow | C11 ⋊ C5×ΓL(1,𝔽16) |
| Sylow | C3 ⋊ AGL(1,𝔽5)×C11⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C5×C11 | C4×C5 |
| prime radical | C3×D5×C11⋊C5 | C2 |
| cosocle | C3×D5×C11 | C2×C5 |
| LCS | G ▷ C3×C5×C11 | |
| UCS | C1 | |
52 conjugacy classes of subgroups.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 165 |
63 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3300, 71);