Finite Group DatabasebetaFinite Group Databasebeta| order | 1188 |
| isoclinism | isoclinic class of #272 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×#1084 |
| derived, Sylow | H(3,𝔽3) ⋊ C4×C11 |
| Hall | C11×H(3,𝔽3) ⋊ C4 |
66 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 396 |
A minimal faithful permutation representation — 3 generators on 24 points:
(1,2,3,4,5,6,7,8,9,10,11)(13,15)(16,20)(17,19)(21,22,23,24);(13,16,17)(15,19,20);(12,13,15)(14,17,19)(16,20,18)220 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1188, 23);