Finite Group DatabasebetaFinite Group Databasebeta| order | 1188 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C32 |
| direct product | H(3,𝔽3)×Dic11 |
| unambiguous semidirect product | C11⋊(C4×H(3,𝔽3)) |
| unambiguous semidirect product | (C32×Dic11)⋊C3 |
| Hall | C11×H(3,𝔽3) ⋊ C4 |
| Sylow | C11 ⋊ C4×H(3,𝔽3) |
66 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 396 |
A minimal faithful permutation representation — 2 generators on 24 points:
(1,2,4)(3,6,8)(5,9,7)(10,11)(12,13)(14,15,16,17,18,19,20,21,22,23,24);(2,5,6)(4,8,9)(10,12,11,13)(15,24)(16,23)(17,22)(18,21)(19,20)154 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1188, 12);