Finite Group DatabasebetaFinite Group Databasebeta| order | 1176 |
| isoclinism | isoclinic class of C3⋊#5997 |
| automorphism | ? |
| homology | Abelianization (H1) = C8 · Schur multiplier (H2) = C7 |
| unambiguous semidirect product | C3⋊#87637 |
| derived, Hall | C3×C72 ⋊ C8 |
| Sylow | C72 ⋊ C3⋊C8 |
| Sylow | C3 ⋊ #87637 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C3⋊#5997 |
| commutator, hypocenter | C3×C72 | C8 |
| Fitting, socle, prime radical | C2×C3×C72 | C4 |
| cosocle | C3×C7⋊Dic7 | C2 |
| LCS | G ▷ C3×C72 | |
| UCS | C1 ◁ C2 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 168 |
Polycyclic presentation:
2^3,3,7^2|a^2=b,b^2=c,d^a=d^2,e^a=e^3f^5,f^a=e^5f^4,e^b=e^6,f^b=f^684 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1176, 139);