Finite Group DatabasebetaFinite Group Databasebeta| order | 1188 |
| isoclinism | isoclinic class of C3⋊(C3⋊D33) |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C33 |
| direct product | C2×C3⋊(C3⋊D33) |
| unambiguous semidirect product | (C2×C3)⋊(C3⋊D33) |
| unambiguous semidirect product | (C2×C11)⋊(C3⋊(C3⋊D3)) |
| Fitting, socle | C2×C33×C11 ⋊ C2 |
| derived, Hall | C33×C11 ⋊ C22 |
| Sylow | C33 ⋊ C2×D11 |
| Sylow | C11 ⋊ C2×C3⋊(C3⋊D3) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C3⋊(C3⋊D33) |
| commutator, cosocle, hypocenter | C33×C11 | C22 |
| Frattini | C1 | G |
| Fitting, socle | C2×C33×C11 | C2 |
| LCS | G ▷ C33×C11 | |
| UCS | C1 ◁ C2 | |
280 conjugacy classes of subgroups.
| transitive degree | μt(G) = 594 |
300 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1188, 98);