Finite Group DatabasebetaFinite Group Databasebeta| order | 876 |
| isoclinism | isoclinic class of #64408⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #64408⋊C3 |
| Fitting, socle, derived, Sylow | C73 ⋊ C3×C4 |
| Hall | #64408 ⋊ C3 |
| Hall | C73⋊C3 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C73 | C3×C4 |
| prime radical | D73⋊C3 | C2 |
| cosocle | D73 | C2×C3 |
| LCS | G ▷ C73 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 73 |
Polycyclic presentation:
2,3,2,73|a^2=c,d^a=d^27,d^b=d^8,d^c=d^7218 conjugacy classes — view the full character table.
| maximal subgroup of | #10596842⋊C3, C2×#64408⋊C3, #14581496, … |
| maximal normal subgroup of | #10596842⋊C3, C2×#64408⋊C3, #14581496, … |
| maximal quotient of | #10596833⋊C3, C2×#64408⋊C3, #14581472, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(876, 7);