Finite Group DatabasebetaFinite Group Databasebeta| order | 1188 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C11⋊#1084 |
| derived, Hall | C11×H(3,𝔽3) ⋊ C4 |
| Sylow | H(3,𝔽3) ⋊ Dic11 |
| Sylow | C11 ⋊ #1084 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2×C3 | C3⋊D33 |
| commutator, hypocenter | C11×H(3,𝔽3) | C4 |
| Fitting, prime radical, cosocle | C2×C11×H(3,𝔽3) | C2 |
| socle | C2×C3×C11 | C3⋊D3 |
| LCS | G ▷ C11×H(3,𝔽3) | |
| UCS | C1 ◁ C2×C3 | |
66 conjugacy classes of subgroups.
| transitive degree | μt(G) = 396 |
Polycyclic presentation:
2^2,3^2,11,3|a^2=b,c^a=c^2,d^a=d^2,e^a=e^10,d^c=df130 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1188, 25);