Finite Group DatabasebetaFinite Group Databasebeta| order | 1176 |
| isoclinism | isoclinic class of C3⋊#87656 |
| automorphism | ? |
| homology | Abelianization (H1) = C8 · Schur multiplier (H2) = C7 |
| unambiguous semidirect product | C3⋊#87656 |
| Fitting, socle, derived, Hall | C3×C72 ⋊ C8 |
| Sylow | C72 ⋊ C3⋊C8 |
| Sylow | C3 ⋊ #87656 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C72 | C8 |
| prime radical | C3×C7⋊D7 | C4 |
| cosocle | C3×#5997 | C2 |
| LCS | G ▷ C3×C72 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 84 |
Polycyclic presentation:
2^3,3,7^2|a^2=b,b^2=c,d^a=d^2,e^a=e^4f^5,f^a=e^6f^6,e^b=e^4f,f^b=e^4f^3,e^c=e^6,f^c=f^630 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1176, 230);