Finite Group DatabasebetaFinite Group Databasebeta| order | 24642 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C37 · Schur multiplier (H2) = C1 |
| direct product | C37×C3⋊(D37⋊C3) |
| unambiguous semidirect product | C3⋊(C37×D37⋊C3) |
| unambiguous semidirect product | (C37⋊C3)⋊(D3×C37) |
| unambiguous semidirect product | D111⋊(C3×C37) |
| Fitting, socle | C3×C372 ⋊ C2×C3 |
| derived | C3×C37 ⋊ C2×C3×C37 |
| Hall | C3×C37×C37⋊C3 ⋊ C2 |
| Sylow | C372 ⋊ C3×D3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C37 | C3⋊(D37⋊C3) |
| commutator, cosocle, hypocenter | C3×C37 | C2×C3×C37 |
| Frattini | C1 | G |
| Fitting, socle | C3×C372 | C2×C3 |
| LCS | G ▷ C3×C37 | |
| UCS | C1 ◁ C37 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 666 |
999 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24642, 78);