Finite Group DatabasebetaFinite Group Databasebeta| order | 18564 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C13⋊C3×C7⋊#595 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C7×C13×C17 | C3×C4 |
| prime radical | C7×D17×C13⋊C3 | C2 |
| cosocle | C7×C13×D17 | C2×C3 |
| LCS | G ▷ C7×C13×C17 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1547 |
266 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18564, 124);