Finite Group DatabasebetaFinite Group Databasebeta| order | 18564 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | ((C13⋊C3)⋊D7)⋊D17 |
| unambiguous semidirect product | (C17⋊(D13⋊C3))⋊D7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C7×C13×C17 | C22×C3 |
| LCS | G ▷ C7×C13×C17 | |
| UCS | C1 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1547 |
Polycyclic presentation:
2^2,3,7,13,17|e^a=e^12,f^a=f^16,d^b=d^6,e^b=e^12,e^c=e^3272 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18564, 123);