Finite Group DatabasebetaFinite Group Databasebeta| order | 27684 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #15690484⋊C9 |
| derived, Sylow | C769 ⋊ C4×C9 |
| Hall | C769⋊C9 ⋊ C4 |
| Hall | #15690484 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | #15690484⋊C3 |
| commutator, hypocenter | C769 | C4×C9 |
| Fitting, socle | C3×C769 | C3×C4 |
| prime radical, cosocle | C3×D769 | C2×C3 |
| LCS | G ▷ C769 | |
| UCS | C1 ◁ C3 | |
18 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6921 |
Polycyclic presentation:
2,3,2,769,3|a^2=c,b^3=e,d^a=d^707,d^b=d^360,d^c=d^768228 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27684, 8);