Finite Group DatabasebetaFinite Group Databasebeta| order | 24642 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
| direct product | C3×D1369⋊C3 |
| unambiguous semidirect product | D1369⋊C32 |
| unambiguous semidirect product | (C1369⋊C3)⋊(C2×C3) |
| unambiguous semidirect product | (C3×D1369)⋊C3 |
| Fitting | C3×C1369 ⋊ C2×C3 |
| derived, Sylow | C1369 ⋊ C2×C32 |
| Hall | C3×C1369⋊C3 ⋊ C2 |
| Hall | D1369 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D1369⋊C3 |
| commutator, cosocle, hypocenter | C1369 | C2×C32 |
| Frattini | C37 | C3×D37⋊C3 |
| Fitting | C3×C1369 | C2×C3 |
| socle | C3×C37 | D37⋊C3 |
| LCS | G ▷ C1369 | |
| UCS | C1 ◁ C3 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4107 |
702 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24642, 10);