Finite Group DatabasebetaFinite Group Databasebeta| order | 3540 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D5×D177 |
| unambiguous semidirect product | (C3×D5)⋊D59 |
| unambiguous semidirect product | (D5×C59)⋊D3 |
| Fitting, socle, derived, Hall | C3×C5×C59 ⋊ C22 |
| Hall | C5×C59 ⋊ C2×D3 |
| Hall | C3×C59 ⋊ C2×D5 |
| Sylow | C59 ⋊ D3×D5 |
| Hall | C3×C5 ⋊ C2×D59 |
| Sylow | C5 ⋊ C2×D177 |
| Sylow | C3 ⋊ D5×D59 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C5×C59 | C22 |
| LCS | G ▷ C3×C5×C59 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| minimal degree | μ(G) = 67 |
| transitive degree | μt(G) = 885 |
360 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D25×D177, C5×D5×D177, C5⋊D5×D177, … |
| maximal normal subgroup of | C5×D5×D177, C7×D5×D177 |
| maximal quotient of | D25×D177, C5×D5×D177, C5⋊D5×D177, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3540, 18);