Finite Group DatabasebetaFinite Group Databasebeta| order | 876 |
| isoclinism | isoclinic class of C3⋊#64408 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊#64408 |
| Fitting, socle, derived, Hall | C3×C73 ⋊ C4 |
| Sylow | C73 ⋊ Dic3 |
| Sylow | C3 ⋊ #64408 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C73 | C4 |
| prime radical, cosocle | C3×D73 | C2 |
| LCS | G ▷ C3×C73 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
| minimal degree | μ(G) = 76 |
| transitive degree | μt(G) = 219 |
Polycyclic presentation:
2^2,3,73|a^2=b,c^a=c^2,d^a=d^46,d^b=d^7260 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#64408, C2×C3⋊#64408, C9⋊#64408, … |
| maximal normal subgroup of | D3×#64408, C2×C3⋊#64408, C3⋊(#64408⋊C3), … |
| maximal quotient of | C3⋊#10596833, C2×C3⋊#64408, C9⋊#64408, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(876, 10);