Finite Group DatabasebetaFinite Group Databasebeta| order | 26862 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C112 · Schur multiplier (H2) = C11 |
| direct product | C112×D111 |
| unambiguous semidirect product | C3⋊(C112×D37) |
| unambiguous semidirect product | C37⋊(D3×C112) |
| Fitting, socle, Hall | C3×C112×C37 ⋊ C2 |
| derived, Hall | C3×C37 ⋊ C2×C112 |
| Hall | C112×C37 ⋊ D3 |
| Hall | C3×C112 ⋊ D37 |
| Sylow | C37 ⋊ D3×C112 |
| Sylow | C3 ⋊ C112×D37 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C112 | D111 |
| commutator, cosocle, hypocenter | C3×C37 | C2×C112 |
| Frattini | C1 | G |
| Fitting, socle | C3×C112×C37 | C2 |
| LCS | G ▷ C3×C37 | |
| UCS | C1 ◁ C112 | |
112 conjugacy classes of subgroups.
| transitive degree | μt(G) = 13431 |
6897 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26862, 36);