Finite Group DatabasebetaFinite Group Databasebeta| order | 4588 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D31×D37 |
| unambiguous semidirect product | (C37×D31)⋊C2 |
| unambiguous semidirect product | (C31×D37)⋊C2 |
| unambiguous semidirect product | D1147⋊C2 |
| Fitting, socle, derived, Hall | C31×C37 ⋊ C22 |
| Sylow | C37 ⋊ C2×D31 |
| Sylow | C31 ⋊ C2×D37 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C31×C37 | C22 |
| LCS | G ▷ C31×C37 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
| minimal degree | μ(G) = 68 |
| transitive degree | μt(G) = 1147 |
340 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #20293709⋊C2, #20293708⋊C2, D37×D31⋊C3, … |
| maximal normal subgroup of | #20293709⋊C2, #20293708⋊C2, D37×D31⋊C3, … |
| maximal quotient of | C3×D31×D37, D37×D93, D31×D111, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4588, 8);