Finite Group DatabasebetaFinite Group Databasebeta| order | 27549 |
| automorphism | ? |
| homology | Abelianization (H1) = C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C3061 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | C3061⋊C3 |
| commutator, hypocenter | C3061 | C9 |
| Fitting, socle, prime radical, cosocle | C3×C3061 | C3 |
| LCS | G ▷ C3061 | |
| UCS | C1 ◁ C3 | |
6 conjugacy classes of subgroups.
| transitive degree | μt(G) = 27549 |
Polycyclic presentation:
3^2,3061|a^3=b,c^a=c^5613069 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27549, 1);