Finite Group DatabasebetaFinite Group Databasebeta| order | 18564 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C13 · Schur multiplier (H2) = C2 |
| direct product | C13×D17×D21 |
| unambiguous semidirect product | (C3×D17)⋊(C13×D7) |
| unambiguous semidirect product | (C7×D17)⋊(D3×C13) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13 | D17×D21 |
| commutator, cosocle, hypocenter | C3×C7×C17 | C22×C13 |
| Frattini | C1 | G |
| Fitting, socle | C3×C7×C13×C17 | C22 |
| LCS | G ▷ C3×C7×C17 | |
| UCS | C1 ◁ C13 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4641 |
1560 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18564, 186);