Finite Group DatabasebetaFinite Group Databasebeta| order | 4596 |
| automorphism | Aut(G) order 1755672 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| dihedral | D2298 |
| direct product | C2×D1149 |
| unambiguous semidirect product | (C2×C3)⋊D383 |
| unambiguous semidirect product | (C2×C383)⋊D3 |
| Fitting, socle | C2×C3×C383 ⋊ C2 |
| derived, Hall | C3×C383 ⋊ C22 |
| Sylow | C383 ⋊ C2×D3 |
| Sylow | C3 ⋊ C2×D383 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D1149 |
| commutator, cosocle, hypocenter | C3×C383 | C22 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C383 | C2 |
| LCS | G ▷ C3×C383 | |
| UCS | C1 ◁ C2 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2298 |
1152 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×D3447, D3×D1149, C2×C3⋊D1149, … |
| maximal normal subgroup of | C2×C3×D1149, C2×C5×D1149, C2×C7×D1149, … |
| maximal quotient of | C2×D3447, D3×D1149, C2×C3⋊D1149, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4596, 8);