Finite Group DatabasebetaFinite Group Databasebeta| order | 18564 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C17 · Schur multiplier (H2) = C2 |
| direct product | C17×#10587717⋊C2 |
| unambiguous semidirect product | #10587717⋊(C2×C17) |
| unambiguous semidirect product | #10587721⋊(C2×C17) |
| unambiguous semidirect product | #10587723⋊(C2×C17) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C17 | #10587717⋊C2 |
| commutator, cosocle, hypocenter | C7×C13 | C22×C3×C17 |
| Frattini | C1 | G |
| Fitting, socle | C7×C13×C17 | C22×C3 |
| LCS | G ▷ C7×C13 | |
| UCS | C1 ◁ C17 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1547 |
408 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18564, 75);