Finite Group DatabasebetaFinite Group Databasebeta| order | 876 |
| isoclinism | isoclinic class of C73⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C4×C73⋊C3 |
| unambiguous semidirect product | (C4×C73)⋊C3 |
| Fitting, Hall | C4×C73 ⋊ C3 |
| derived, Sylow | C73 ⋊ C3×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | C73⋊C3 |
| commutator, hypocenter | C73 | C3×C4 |
| Frattini | C2 | C2×C73⋊C3 |
| Fitting | C4×C73 | C3 |
| socle, cosocle | C2×C73 | C2×C3 |
| prime radical | C2×C73⋊C3 | C2 |
| LCS | G ▷ C73 | |
| UCS | C1 ◁ C4 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 292 |
108 conjugacy classes — view the full character table.
| maximal subgroup of | #10596831⋊C3, C8×C73⋊C3, (C73⋊C3)⋊Q8, … |
| maximal normal subgroup of | #10596831⋊C3, C8×C73⋊C3, (C73⋊C3)⋊Q8, … |
| maximal quotient of | C8×C73⋊C3, C2×C4×C73⋊C3, C4×#10620321, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(876, 2);