Finite Group DatabasebetaFinite Group Databasebeta| order | 4596 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C2×C3×D383 |
| unambiguous semidirect product | C383⋊(C22×C3) |
| unambiguous semidirect product | (C2×C383)⋊(C2×C3) |
| Fitting, socle | C2×C3×C383 ⋊ C2 |
| derived, Sylow | C383 ⋊ C22×C3 |
| Hall | C3×C383 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | D383 |
| commutator, cosocle, hypocenter | C383 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C383 | C2 |
| LCS | G ▷ C383 | |
| UCS | C1 ◁ C2×C3 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2298 |
1158 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C9×D383, C3×D3×D383, C2×C3×D1149, … |
| maximal normal subgroup of | C2×C9×D383, C2×C32×D383, C2×C3×C5×D383, … |
| maximal quotient of | C2×C9×D383, C3×D3×D383, C2×C3×D1149, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4596, 10);