Finite Group DatabasebetaFinite Group Databasebeta| order | 1176 |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | Q8⋊#3861 |
| Fitting, derived, Hall | C72×Q8 ⋊ C3 |
| Sylow | C72 ⋊ SL(2,𝔽3) |
| Sylow | Q8 ⋊ #3861 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C22⋊#3861 |
| commutator, Fitting, cosocle, hypocenter | C72×Q8 | C3 |
| socle | C2×C72 | A4 |
| LCS | G ▷ C72×Q8 | |
| UCS | C1 ◁ C2 | |
70 conjugacy classes of subgroups.
| transitive degree | μt(G) = 392 |
Polycyclic presentation:
3,2^2,7^2,2|b^2=f,c^2=f,b^a=c,c^a=bc,d^a=d^4,e^a=e^4,c^b=cf87 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1176, 182);