Finite Group DatabasebetaFinite Group Databasebeta| order | 4588 |
| automorphism | Aut(G) order 2477520 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| dihedral | D2294 |
| direct product | C2×D1147 |
| unambiguous semidirect product | (C2×C31)⋊D37 |
| unambiguous semidirect product | (C2×C37)⋊D31 |
| Fitting, socle | C2×C31×C37 ⋊ C2 |
| derived, Hall | C31×C37 ⋊ C22 |
| Sylow | C37 ⋊ C2×D31 |
| Sylow | C31 ⋊ C2×D37 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D1147 |
| commutator, cosocle, hypocenter | C31×C37 | C22 |
| Frattini | C1 | G |
| Fitting, socle | C2×C31×C37 | C2 |
| LCS | G ▷ C31×C37 | |
| UCS | C1 ◁ C2 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2294 |
1150 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#20293717, C2×#20293716, C2×(C31⋊C3)⋊D37, … |
| maximal normal subgroup of | C2×#20293717, C2×#20293716, C2×(C31⋊C3)⋊D37, … |
| maximal quotient of | D3×D1147, C2×D3441, C2×C3×D1147, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4588, 9);