Finite Group DatabasebetaFinite Group Databasebeta| order | 7611 |
| isoclinism | isoclinic class of C43⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C59 · Schur multiplier (H2) = C1 |
| direct product | C59×C43⋊C3 |
| unambiguous semidirect product | C43⋊(C3×C59) |
| unambiguous semidirect product | (C43×C59)⋊C3 |
| Fitting, socle, Hall | C43×C59 ⋊ C3 |
| derived, Sylow | C43 ⋊ C3×C59 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C59 | C43⋊C3 |
| commutator, hypocenter | C43 | C3×C59 |
| Frattini | C1 | G |
| Fitting, socle | C43×C59 | C3 |
| LCS | G ▷ C43 | |
| UCS | C1 ◁ C59 | |
8 conjugacy classes of subgroups.
1003 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C59×C43⋊C3, D59×C43⋊C3, C59×D43⋊C3, … |
| maximal normal subgroup of | C2×C59×C43⋊C3, D59×C43⋊C3, C59×D43⋊C3, … |
| maximal quotient of | C2×C59×C43⋊C3, C59×C43⋊C9, C3×C59×C43⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7611, 1);