Finite Group DatabasebetaFinite Group Databasebeta| order | 18564 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | ΓL(1,𝔽8)⋊#11725131 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C7×C13×C17 | C3×C4 |
| prime radical | ΓL(1,𝔽8)×D221 | C2 |
| cosocle | C7×D221 | C2×C3 |
| LCS | G ▷ C7×C13×C17 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1547 |
Polycyclic presentation:
2,3,2,7,13,17|a^2=c,d^a=d^6,e^a=e^5,f^a=f^4,d^b=d^2,e^c=e^12,f^c=f^16289 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18564, 81);