Finite Group DatabasebetaFinite Group Databasebeta| order | 27549 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C3 |
| direct product | C3×C3061⋊C3 |
| unambiguous semidirect product | C3061⋊C32 |
| unambiguous semidirect product | (C3×C3061)⋊C3 |
| Fitting, socle | C3×C3061 ⋊ C3 |
| derived, Sylow | C3061 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C3061⋊C3 |
| commutator, cosocle, hypocenter | C3061 | C32 |
| Frattini | C1 | G |
| Fitting, socle | C3×C3061 | C3 |
| LCS | G ▷ C3061 | |
| UCS | C1 ◁ C3 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9183 |
3069 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27549, 4);