Finite Group DatabasebetaFinite Group Databasebeta| order | 876 |
| isoclinism | isoclinic class of D73 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C2×C3×D73 |
| Fitting, socle | C2×C3×C73 ⋊ C2 |
| derived, Sylow | C73 ⋊ C22×C3 |
| Hall | C3×C73 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | D73 |
| commutator, cosocle, hypocenter | C73 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C73 | C2 |
| LCS | G ▷ C73 | |
| UCS | C1 ◁ C2×C3 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 438 |
228 conjugacy classes — view the full character table.
| maximal subgroup of | Dic3×D73, #13182118, #13182119, … |
| maximal normal subgroup of | Dic3×D73, #13182118, #13182119, … |
| maximal quotient of | C3×Dic146, C3×C4×D73, C3×D292, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(876, 15);