Finite Group DatabasebetaFinite Group Databasebeta| order | 1188 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(3,𝔽3) |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4×C11 · Schur multiplier (H2) = C32 |
| direct product | C4×C11×H(3,𝔽3) |
| unambiguous semidirect product | (C32×C4)⋊(C3×C11) |
| unambiguous semidirect product | (C32×C4×C11)⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center | C3×C4×C11 | C32 |
| commutator | C3 | C32×C4×C11 |
| Frattini, cosocle | C2×C3 | C2×C32×C11 |
| socle | C2×C3×C11 | C2×C32 |
| prime radical | C2×C11×H(3,𝔽3) | C2 |
| LCS | G ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C3×C4×C11 ◁ G | |
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:
(1,2,3,4)(5,6,7,8,9,10,11,12,13,14,15)(16,17,19)(18,21,23)(20,24,22);(17,20,21)(19,23,24)484 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1188, 27);