Finite Group DatabasebetaFinite Group Databasebeta| order | 16644 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C2×#22552251 |
| Fitting, socle | C2×C19×C73 ⋊ C2×C3 |
| derived, Hall | C19×C73 ⋊ C22×C3 |
| Hall | C2×D1387 ⋊ C3 |
| Hall | #16861931 ⋊ C22 |
| Sylow | C73 ⋊ C2×D19⋊C3 |
| Sylow | C19 ⋊ C2×D73⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #22552251 |
| commutator, cosocle, hypocenter | C19×C73 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C19×C73 | C2×C3 |
| LCS | G ▷ C19×C73 | |
| UCS | C1 ◁ C2 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2774 |
474 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16644, 40);