Finite Group DatabasebetaFinite Group Databasebeta| order | 1176 |
| isoclinism | isoclinic class of #5997⋊D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #5997⋊D3 |
| Fitting, socle, Hall | C3×C72 ⋊ D4 |
| Sylow | C72 ⋊ D12 |
| Sylow | C3 ⋊ #5997⋊C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle | C3×C7⋊D7 | C22 |
| Fitting, socle, hypocenter | C3×C72 | D4 |
| LCS | G ▷ C3×C7⋊D7 ▷ C3×C72 | |
| UCS | C1 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 42 |
Polycyclic presentation:
2^3,3,7^2|b^2=c,b^a=bc,d^a=d^2,e^a=e^6,e^b=f^6,f^b=e,e^c=e^6,f^c=f^636 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1176, 234);