Finite Group DatabasebetaFinite Group Databasebeta| order | 876 |
| isoclinism | isoclinic class of D73⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C2×D73⋊C3 |
| unambiguous semidirect product | D73⋊(C2×C3) |
| unambiguous semidirect product | (C73⋊C3)⋊C22 |
| unambiguous semidirect product | (C2×D73)⋊C3 |
| unambiguous semidirect product | (C2×C73⋊C3)⋊C2 |
| Fitting, socle | C2×C73 ⋊ C2×C3 |
| derived, Sylow | C73 ⋊ C22×C3 |
| Hall | C2×D73 ⋊ C3 |
| Hall | C73⋊C3 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D73⋊C3 |
| commutator, cosocle, hypocenter | C73 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C73 | C2×C3 |
| LCS | G ▷ C73 | |
| UCS | C1 ◁ C2 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 146 |
36 conjugacy classes — view the full character table.
| maximal subgroup of | C4×D73⋊C3, C4⋊(D73⋊C3), (C22⋊D73)⋊C3, … |
| maximal normal subgroup of | C4×D73⋊C3, C4⋊(D73⋊C3), (C22⋊D73)⋊C3, … |
| maximal quotient of | (C73⋊C3)⋊Q8, C4×D73⋊C3, C4⋊(D73⋊C3), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(876, 8);