Finite Group DatabasebetaFinite Group Databasebeta| order | 6660 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | ΓL(1,𝔽16)×C37⋊C3 |
| unambiguous semidirect product | C3⋊(AGL(1,𝔽5)×C37⋊C3) |
| unambiguous semidirect product | (C37×ΓL(1,𝔽16))⋊C3 |
| Fitting, socle, derived | C3×C5×C37 ⋊ C3×C4 |
| Hall | C3×C5×C37⋊C3 ⋊ C4 |
| Hall | C3×C37⋊C3 ⋊ AGL(1,𝔽5) |
| Hall | C5×C37 ⋊ C3×Dic3 |
| Sylow | C37 ⋊ C3×ΓL(1,𝔽16) |
| Sylow | C5 ⋊ Dic3×C37⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C5×C37 | C3×C4 |
| LCS | G ▷ C3×C5×C37 | |
| UCS | C1 | |
56 conjugacy classes of subgroups.
135 conjugacy classes — view the full character table.
| maximal subgroup of | C37⋊C3×C3⋊#1035, C5×ΓL(1,𝔽16)×C37⋊C3, C37⋊C3×C3⋊#1042, … |
| maximal normal subgroup of | C5×ΓL(1,𝔽16)×C37⋊C3 |
| maximal quotient of | C37⋊C3×C3⋊#1035, C5×ΓL(1,𝔽16)×C37⋊C3, C37⋊C3×C3⋊#1042, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6660, 100);