Finite Group DatabasebetaFinite Group Databasebeta| order | 3588 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C3×C23⋊#261 |
| unambiguous semidirect product | C23⋊(C3×#261) |
| Fitting, socle, Hall | C3×C13×C23 ⋊ C4 |
| derived, Hall | C13×C23 ⋊ C3×C4 |
| Hall | C3×C23 ⋊ #261 |
| Hall | C3×C13 ⋊ Dic23 |
| Sylow | C23 ⋊ C3×#261 |
| Sylow | C13 ⋊ C3×Dic23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C23⋊#261 |
| commutator, hypocenter | C13×C23 | C3×C4 |
| Frattini | C1 | G |
| Fitting, socle | C3×C13×C23 | C4 |
| prime radical | C3×C23×D13 | C2 |
| cosocle | C23×D13 | C2×C3 |
| LCS | G ▷ C13×C23 | |
| UCS | C1 ◁ C3 | |
24 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 897 |
285 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C5×C23⋊#261, C3×C23⋊#63122, C3×C23⋊#63121, … |
| maximal normal subgroup of | C3×C5×C23⋊#261, C3×C7×C23⋊#261 |
| maximal quotient of | C3×C5×C23⋊#261, C3×C23⋊#63122, C3×C23⋊#63121, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3588, 21);